diff --git a/TFGChang/AeroForcesCalculation.m b/TFGChang/AeroForcesCalculation.m
new file mode 100644
index 0000000000..f324a9df4c
--- /dev/null
+++ b/TFGChang/AeroForcesCalculation.m
@@ -0,0 +1 @@
+classdef AeroForcesCalculation < handle

    properties (Access = public)
        L
        D
        E
    end

    properties (Access = private)
        mesh
        nodesConditions
        pressureFun
    end

    properties (Access = private)
        connec
        bMesh
        pBoundary
        normalVectors
        lengthElement
        centroid
        centralPointsElement
        nX
        nY
    end

    methods (Access = public)

        function obj = AeroForcesCalculation(cParams)
            obj.init(cParams);
            obj.identifyBoundaryEdges();
            obj.createBoundaryMesh();
            obj.assignPressureToBoundary();
            obj.defineVariables();
        end

        function compute(obj)
            obj.computeNormalVectors();
            obj.convertNorVectorsToLanFunctions();
            obj.computeDragForces();
            obj.computeLiftForces();
            obj.computeEfficiency();
            %obj.plotResults();
        end

    end

    methods (Access = private)

        function init(obj,cParams)
            obj.mesh              = cParams.mesh;
            obj.nodesConditions   = cParams.nodesConditions;
            obj.pressureFun       = cParams.pressureFun;
        end

        function identifyBoundaryEdges(obj)
            obj.mesh.computeEdges();
            e  = obj.mesh.edges.nodesInEdges;
            bE = ismember(e,obj.nodesConditions);
            bEIndices = find(prod(bE,2));
            obj.connec = e(bEIndices,:);
        end

        function createBoundaryMesh(obj)
            ss.coord    = obj.mesh.coord;
            ss.connec   = obj.connec;
            ss.kFace    = -1;
            obj.bMesh   = Mesh.create(ss);
            obj.bMesh   = obj.bMesh.computeCanonicalMesh();
        end

        function assignPressureToBoundary(obj)
            obj.pBoundary = LagrangianFunction.create(obj.bMesh,1,obj.pressureFun.order);
            pVals         = obj.pressureFun.fValues(obj.nodesConditions,1);
            obj.pBoundary.setFValues(pVals);
        end

        function plotPressureDistribution(obj)
            obj.pBoundary.plot();
        end

        function defineVariables(obj)
            obj.normalVectors        = zeros(obj.bMesh.nelem,obj.bMesh.ndim);
            obj.lengthElement        = zeros(obj.bMesh.nelem,1);
            obj.centroid             = mean(obj.bMesh.coord);
            obj.centralPointsElement = (obj.bMesh.coord(obj.bMesh.connec(:,1),:) + obj.bMesh.coord(obj.bMesh.connec(:,2),:))/2;
        end

        function computeNormalVectors(obj)
            node1               = obj.bMesh.coord(obj.bMesh.connec(:,1),:);
            node2               = obj.bMesh.coord(obj.bMesh.connec(:,2),:);
            distanceNodes       = node2 - node1;
            obj.lengthElement   = vecnorm(distanceNodes,2,2);
            tanVector           = distanceNodes./obj.lengthElement;
            obj.normalVectors   = tanVector * [0 1;-1 0];
        end

        function convertNorVectorsToLanFunctions(obj)
            obj.nX = LagrangianFunction.create(obj.bMesh,1,'P0');
            obj.nY = LagrangianFunction.create(obj.bMesh,1,'P0');
            obj.nX.setFValues(obj.normalVectors(:,1));
            obj.nY.setFValues(obj.normalVectors(:,2));
        end

        function computeDragForces(obj)
            s.operation = @(x) -obj.pBoundary.evaluate(x).*obj.nX.evaluate(x);
            s.mesh      = obj.mesh;
            pNX         = DomainFunction(s);
            obj.D       = Integrator.compute(pNX,obj.bMesh,2);
        end

        function computeLiftForces(obj)
            s.operation = @(x) -obj.pBoundary.evaluate(x).*obj.nY.evaluate(x);
            s.mesh      = obj.mesh;
            pNY         = DomainFunction(s);
            obj.L       = Integrator.compute(pNY,obj.bMesh,2);
        end

        function computeEfficiency(obj)
            obj.E = obj.L/obj.D;
        end

        function plotResults(obj)
            obj.plotPressureDistribution();
            figure;
            quiver(obj.centralPointsElement(:,1),obj.centralPointsElement(:,2),obj.normalVectors(:,1),obj.normalVectors(:,2));
            hold on;
            quiver(obj.centroid(1,1),obj.centroid(1,2),obj.D,0);
            hold on;
            quiver(obj.centroid(1,1),obj.centroid(1,2),0,obj.L);
            hold on;
            obj.bMesh.plot()
            title("Lift and drag distribution");
            xlabel("x");
            ylabel("y");
        end
    end

end
\ No newline at end of file
diff --git a/TFGChang/AeroForcesCalculationTestComputer.m b/TFGChang/AeroForcesCalculationTestComputer.m
new file mode 100644
index 0000000000..09b369755e
--- /dev/null
+++ b/TFGChang/AeroForcesCalculationTestComputer.m
@@ -0,0 +1,78 @@
+classdef AeroForcesCalculationTestComputer < handle
+
+    properties (Access = public)
+        comparingLiftMessage
+        comparingDragMessage
+    end
+
+    properties (Access = private)
+        tolerance
+    end
+
+    properties (Access = private)
+        LiftOriginal
+        DragOriginal
+        LiftTest
+        DragTest
+    end
+    
+    methods (Access = public)
+
+        function obj = AeroForcesCalculationTestComputer(cParams)
+            obj.init(cParams);
+        end
+
+        function compute(obj)
+            obj.compareLift();
+            obj.compareDrag();
+            result = [obj.comparingLiftMessage, newline, obj.comparingDragMessage];
+            disp(result);
+        end
+
+    end
+
+
+    methods (Access = private)
+
+        function init(obj,cParams)
+            obj.saveInput(cParams);
+            obj.loadOriginalfinalMesh();
+            obj.tolerance = 1e-4;
+        end
+
+        function saveInput(obj,cParams)
+            obj.LiftTest    = cParams.L;
+            obj.DragTest    = cParams.D;
+        end
+
+        function loadOriginalfinalMesh(obj)
+            load("E_GF_N2412.mat","Li","Di");
+            obj.LiftOriginal = Li;
+            obj.DragOriginal = Di;
+        end
+
+        function compareLift(obj)
+            try
+                relativeError = abs(obj.LiftOriginal - obj.LiftTest) / abs(obj.LiftOriginal);
+                assert(relativeError < obj.tolerance, ...
+                    sprintf('The lift force does not match the expected value.\nRelative error: %.4f', relativeError));
+                obj.comparingLiftMessage = 'The lift force corresponds to the expected value.';
+            catch ME
+                obj.comparingLiftMessage = ME.message;
+            end
+        end
+
+        function compareDrag(obj)
+            try
+                relativeError = abs(obj.DragOriginal - obj.DragTest) / abs(obj.DragOriginal);
+                assert(relativeError < obj.tolerance, ...
+                    sprintf('The drag force does not match the expected value.\nRelative error: %.4f', relativeError));
+                obj.comparingDragMessage = 'The drag force corresponds to the expected value.';
+            catch ME
+                obj.comparingDragMessage = ME.message;
+            end
+        end
+
+    end
+    
+end
\ No newline at end of file
diff --git a/TFGChang/AirfoilOptimizer.m b/TFGChang/AirfoilOptimizer.m
new file mode 100644
index 0000000000..abd1eb3112
--- /dev/null
+++ b/TFGChang/AirfoilOptimizer.m
@@ -0,0 +1,206 @@
+classdef AirfoilOptimizer < handle
+
+    properties (Access = public)
+        optimalParams
+    end
+
+    properties (Access = private)
+        features
+        learningRate
+        optimizer
+        tol
+        upperBC
+        lowerBC
+        ParamsMat
+        E
+        velFunMat
+        PFunMat
+    end
+
+    methods (Access = public)
+
+        function obj = AirfoilOptimizer(cParams)
+            obj.init(cParams);
+        end
+
+        function computeOptAirfoilParams(obj)
+            obj.computeOptimization();
+        end
+
+        function plotEEvolution(obj)
+            obj.plotE();
+        end
+
+        function generateAFSOPVideo(obj)
+            plotFun = @(s, i) AirfoilOptimizer.plotAirfoilContour(s, i);
+            VideoGenerator.compute("AirfoilOptimization", size(obj.ParamsMat,1),100, obj.ParamsMat, plotFun);
+        end
+
+        function generateVelVideo(obj)
+            plotFun = @(s, ~) TestNaca.plotVelocity(s);
+            VideoGenerator.compute('AirfoilOptimization-Velocity', size(obj.velFunMat,2), size(obj.velFunMat,2),obj.velFunMat, plotFun);
+        end
+
+        function generatePVideo(obj)
+            plotFun = @(s, ~) TestNaca.plotPressure(s);
+            VideoGenerator.compute('AirfoilOptimization-Pressure',  size(obj.PFunMat,2), size(obj.PFunMat,2),obj.PFunMat, plotFun);
+        end
+
+        function saveData(obj)
+            save("OptData.mat","obj");
+        end
+
+    end
+
+    methods (Access = private)
+
+        function init(obj,cParams)
+            obj.features                       = cParams.features;
+            obj.optimizer                      = cParams.optimizer;
+            obj.tol                            = cParams.tol;
+            obj.learningRate                   = cParams.learningRate;
+            obj.upperBC                        = cParams.upperBC;
+            obj.lowerBC                        = cParams.lowerBC;
+            obj.optimalParams                  = obj.features;
+            obj.E(1)                           = obj.optimizer.computeOutputValues(obj.optimalParams);
+            obj.ParamsMat(1,:)                 = obj.features;
+            [obj.velFunMat{1}, obj.PFunMat{1}] = computeVelPFun(obj);
+        end
+
+        function projected = projectParams(obj,params)
+            projected     = max(min(params, obj.upperBC), obj.lowerBC);
+            projected(2)  = projected(2) * (projected(1) > 1e-6);
+            projected(1)  = projected(1) * (projected(2) > 1e-6);
+        end
+
+        function computeOptimization(obj)
+            diff     = 1;
+            iter     = 1;
+            maxIter  = 101;%301
+
+            rho      = 0.9;   %0.9 %0.5
+            epsilon  = 1e-8;
+            cache    = zeros(size(obj.optimalParams));
+
+            while diff > obj.tol && iter < maxIter
+
+                % if (iter > 70)
+                %
+                %     obj.learningRate = 0.5;
+                % end
+                %
+                %  if (iter > 97)
+                %
+                %     obj.learningRate = 0.02;
+                %  end
+
+                gradient = obj.optimizer.computeGradient(obj.optimalParams);
+
+                cache = rho * cache + (1 - rho) * (gradient.^2);
+
+                adjustedGradient = obj.learningRate * gradient ./ (sqrt(cache) + epsilon);
+                updatedParams    = obj.optimalParams + adjustedGradient;
+
+                obj.optimalParams = obj.projectParams(updatedParams);
+
+                obj.E(end + 1) = obj.optimizer.computeOutputValues(obj.optimalParams);
+
+                diff = max(abs(obj.ParamsMat(end) - obj.optimalParams));
+
+                obj.ParamsMat(end + 1,:) = obj.optimalParams;
+
+                if mod(iter,2) == 0
+                    [obj.velFunMat{end + 1}, obj.PFunMat{end + 1}] = computeVelPFun(obj);
+                end
+
+                iter = iter + 1;
+            end
+        end
+
+        function plotE(obj)
+            figure;
+            plot(1:length(obj.E), obj.E);
+            xlabel('Iteration');
+            ylabel('Aerodynamic Efficiency');
+            title('Evolution of Airfoil Aerodynamic Efficiency vs Optimization Iteration');
+            grid on;
+        end
+
+        function [velFun,PFun] = computeVelPFun(obj)
+            Naca.flowType = "Stokes";
+            Naca.length   = 8;
+            Naca.height   = 4;
+            Naca.nx       = 420;
+            Naca.M        = obj.optimalParams(1);
+            Naca.p        = obj.optimalParams(2);
+            Naca.t        = obj.optimalParams(3);
+            Naca.chord    = 1;
+            Naca.AoA      = obj.optimalParams(4);
+
+            NacaClass = TestNaca(Naca);
+            NacaClass.compute();
+            velFun = NacaClass.velocityFun;
+            PFun   = NacaClass.pressureFun;
+
+        end
+
+
+    end
+
+    methods (Static)
+
+        function [xContour,yContour] = computeAirfoilContour(s)
+            x   = 0:0.001:1;
+            m   = s(1);
+            p   = s(2);
+            t   = s(3);
+
+            if (m > 1e-6)
+                yc   = (x<=p).*(m/p^2.*(2*p*x - x.^2)) + ...
+                    (x>p).*(m/(1-p)^2.*((1 - 2*p) + 2*p*x - x.^2));
+                dydx = (x<=p).*(2*m/p^2.*(p - x)) + ...
+                    (x>p).*(2*m/(1-p)^2.*(p - x));
+            else
+                yc   = 0;
+                dydx = 0;
+            end
+
+            yt   = 5*t.*(0.2969*sqrt(x)-0.1260*x-0.3516*x.^2+0.2843*x.^3-0.1036*x.^4);
+            theta = atan(dydx);
+
+            xu = x - yt.*sin(theta);
+            yu = yc + yt.*cos(theta);
+            xl = x + yt.*sin(theta);
+            yl = yc - yt.*cos(theta);
+
+            xContour = [xu, fliplr(xl)];
+            yContour = [yu, fliplr(yl)];
+        end
+
+        function [xRot,yRot] = rotateAirfoil(xContour,yContour,AoA)
+            xRot = xContour*cos(AoA) - yContour*sin(AoA);
+            yRot = xContour*sin(AoA) + yContour*cos(AoA);
+        end
+
+        function plotAirfoilContour(s,i)
+
+            AoA = -deg2rad(s(4));
+
+            [xContour,yContour] = AirfoilOptimizer.computeAirfoilContour(s);
+
+            [xRot,yRot] = AirfoilOptimizer.rotateAirfoil(xContour,yContour,AoA);
+
+            plot(xRot, yRot, 'k-', 'LineWidth', 1);
+            xlim([-0.2 1.2]);
+            ylim([-0.6 0.6]);
+            axis equal;
+            xlabel('x'); ylabel('y');
+            title(sprintf('Airfoil Shape Optimization - Iteration %d', i - 1));
+            grid on;
+
+        end
+
+
+    end
+
+end
\ No newline at end of file
diff --git a/TFGChang/Main.m b/TFGChang/Main.m
new file mode 100644
index 0000000000..48368604a3
--- /dev/null
+++ b/TFGChang/Main.m
@@ -0,0 +1,311 @@
+%% Test for TestNaca Stokes
+Naca.flowType  = "Stokes";
+Naca.length      = 8;
+Naca.height      = 4;
+Naca.nx          = 420;
+Naca.M           = 0.02;
+Naca.p           = 0.4;
+Naca.t           = 0.12;
+Naca.chord       = 1;
+Naca.AoA         = 5;
+
+NacaClass = TestNaca(Naca);
+NacaClass.compute();
+NacaClass.print();
+
+%% Test for TestNaca Navier-Stokes (Single Iteration)
+
+Naca.flowType  = "NavierStokes";
+Naca.length    = 8;
+Naca.height    = 4;
+Naca.nx        = 220;
+Naca.M         = 0.09;
+Naca.p         = 0.8;
+Naca.t         = 0.10;
+Naca.chord     = 1;
+Naca.AoA       = 5;
+Naca.nu        = 0.1;
+Naca.convectVel = [];
+
+NacaClass = TestNaca(Naca);
+NacaClass.compute();
+NacaClass.print();
+
+%% Test for TestNaca Navier-Stokes (Progressive Approach)
+Naca.convectVel = [];
+nuRef = [0.1, 1/20, 1/30,1/40, 1/50];
+
+for i = 1 : length(nuRef)
+
+    Naca.flowType  = "NavierStokes";
+    Naca.length    = 8;
+    Naca.height    = 4;
+    Naca.nx        = 220;
+    Naca.M         = 0.09;
+    Naca.p         = 0.8;
+    Naca.t         = 0.10;
+    Naca.chord     = 1;
+    Naca.AoA       = 5;
+    Naca.nu        = nuRef(i);
+
+    NacaClass = TestNaca(Naca);
+    NacaClass.compute();
+    NacaClass.print();
+
+    Naca.convectVel = NacaClass.velocityFun.fValues;
+
+end
+
+%% Test for TestNaca Navier-Stokes (Stabilization Case)
+nuRef = [0.1, 1/20, 1/30,1/40, 1/50];
+
+Naca.flowType  = "Stokes";
+Naca.length      = 8;
+Naca.height      = 4;
+Naca.nx          = 220;%380
+Naca.M           = 0.09;
+Naca.p           = 0.8;
+Naca.t           = 0.10;
+Naca.chord       = 1;
+Naca.AoA         = 5;
+
+NacaClass = TestNaca(Naca);
+NacaClass.compute();
+velValues = NacaClass.velocityFun.fValues;
+
+NodesCoords = NacaClass.velocityFun.mesh.coord;
+
+tol = 1e-10;
+isNodes = @(coor) ismember(coor, NodesCoords, 'rows');
+
+nodes = isNodes(NacaClass.velocityFun.dofCoord);
+iNodes = find(nodes==1);
+dofsNodes = sort(reshape(iNodes, [], 1));
+
+Naca.convectVel = velValues(dofsNodes, :);
+%Naca.convectVel = [];
+
+for i = 1 : length(nuRef)
+
+    tic
+    Naca.flowType  = "NavierStokes";
+    Naca.length    = 8;
+    Naca.height    = 4;
+    Naca.nx        = 220;
+    Naca.M         = 0.09;
+    Naca.p         = 0.8;
+    Naca.t         = 0.10;
+    Naca.chord     = 1;
+    Naca.AoA       = 5;
+    Naca.nu        = nuRef(i);
+
+    disp(i)
+    disp(Naca.nu)
+
+    NacaClass = TestNaca(Naca);
+    NacaClass.compute();
+    NacaClass.print();
+
+    Naca.convectVel = NacaClass.velocityFun.fValues;
+    toc
+end
+
+%% Stokes Flow Control Parameters.
+
+Naca.length = 8;
+Naca.height = 4;
+Naca.nx     = 420;
+Naca.flowType  = "Stokes";
+m     = 0.01:0.01:0.09;
+p     = 0.2:0.1:0.8;
+t     = 0.1:0.02:0.4;
+alpha = -15:1:15;
+
+%% Code to compute Efficiency dataset
+
+% for Symetrical Airfoil
+
+for k = 1:length(t)
+
+    fprintf("m = %f\n", 0.0);
+    fprintf("p = %f\n", 0.2);
+    fprintf("t = %f\n", t(k));
+    Naca.M     = 0.0;
+    Naca.p     = 0.2;
+    Naca.t     = t(k);
+    %t(k);
+    Naca.chord = 1;
+    Naca.AoA   = 12.5;
+
+    NacaClass  = TestNaca(Naca);
+    NacaClass.compute();
+    NacaClass.print();
+end
+
+% for Asymetrical Airfoil
+
+for k = 1:length(t)
+
+    for i = 1:length(m)
+
+        for j = 1:length(p)
+
+            fprintf("m = %f\n", m(i));
+            fprintf("p = %f\n", p(j));
+            fprintf("t = %f\n", t(k));
+            Naca.M     = m(i);
+            Naca.p     = p(j);
+            Naca.t     = t(k);
+            Naca.chord = 1;
+            Naca.AoA   = 12.5;
+
+            NacaClass  = TestNaca(Naca);
+            NacaClass.compute();
+            NacaClass.print();
+
+        end
+
+    end
+end
+
+
+%% Code to compute L,D vs alpha dataset (Stokes Case)
+alpha = 10:0.5:12.5;
+
+for i = 1:length(alpha)
+
+    fprintf("alpha = %f\n", alpha(i));
+    Naca.flowType  = "Stokes";
+    Naca.length    = 8;
+    Naca.height    = 4;
+    Naca.nx        = 420;
+    Naca.M         = 0;
+    Naca.p         = 0;
+    Naca.t         = 0.1;
+    Naca.chord     = 1;
+    Naca.AoA   = alpha(i);
+
+    NacaClass  = TestNaca(Naca);
+    NacaClass.compute();
+    %NacaClass.validate();
+    NacaClass.print();
+
+end
+
+%% Code to compute L,D vs alpha dataset (Navier-Stokes Case)
+alpha = -5:2.5:15;
+Naca.convectVel = [];
+
+for i = 1:length(alpha)
+
+    fprintf("alpha = %f\n", alpha(i));
+    Naca.flowType  = "NavierStokes";
+    Naca.length    = 8;
+    Naca.height    = 4;
+    Naca.nx        = 380;
+    Naca.M         = 0.02;
+    Naca.p         = 0.4;
+    Naca.t         = 0.12;
+    Naca.chord     = 1;
+    Naca.AoA       = -5;
+    Naca.nu        = 0.1;
+    Naca.AoA   = alpha(i);
+
+    NacaClass  = TestNaca(Naca);
+    NacaClass.compute();
+    NacaClass.print();
+
+    Naca.convectVel = [];
+end
+
+%% Plot efficiency vs p and m
+
+data = load('E_AOA0_nx600_PF_FL.txt');
+
+E = data(:, end);
+E = reshape(E, length(p), [])';
+
+[P,M] = meshgrid(p,m);
+
+figure;
+surface(M,P,E);
+shading interp;
+xlabel('Max Camber (m)');
+ylabel('Max Camber Position (p)');
+title('L/D ratio versus Max Camber (m) and Max Camber Position (p)');
+axis tight;
+colorbar;
+caxis([-0.08, 0.08]);
+hold on;
+mesh(M, P, E, 'FaceColor', 'none', 'EdgeColor', 'k', 'LineWidth', 0.5); % Cuadrícula negra
+
+%% Plot L vs alpha and D vs L (Stokes Case)
+
+data = load('LD_N2412_AoA-+15_nx420_PF_NFL.txt');
+
+L = data(:, end-2);
+D = data(:, end-1);
+E = data(:,end);
+
+% Lift figure
+figure;
+plot(alpha, L, 'b');
+xlabel('\alpha (deg)');
+ylabel('Lift (L)');
+title('Lift vs AoA (\alpha)');
+xlim([-15 15]);
+grid on;
+
+% Drag figure
+figure;
+plot(alpha, D, 'r');
+xlabel('\alpha (deg)');
+ylabel('Drag (D)');
+title('Drag vs AoA (\alpha)');
+xlim([-15 15]);
+grid on;
+
+% Efficiency figure
+figure;
+plot(alpha, E, 'g');
+xlabel('\alpha (deg)');
+ylabel('Efficiency (E)');
+title('Efficiency vs AoA (\alpha)');
+xlim([-15 15]);
+grid on;
+
+%% Plot L vs alpha and D vs L (Navier-Stokes Case)
+
+data = load('LDE_NS_RE10.txt');
+alpha = -5:2.5:15;
+
+L = data(:, end-2);
+D = data(:, end-1);
+E = data(:,end);
+
+% Lift figure
+figure;
+plot(alpha, L, 'b');
+xlabel('\alpha (deg)');
+ylabel('Lift (L)');
+title('Lift vs AoA (\alpha)');
+xlim([-5 15]);
+grid on;
+
+% Drag figure
+figure;
+plot(alpha, D, 'r');
+xlabel('\alpha (deg)');
+ylabel('Drag (D)');
+title('Drag vs AoA (\alpha)');
+xlim([-5 15]);
+grid on;
+
+% Efficiency figure
+figure;
+plot(alpha, E, 'g');
+xlabel('\alpha (deg)');
+ylabel('Efficiency (E)');
+title('Efficiency vs AoA (\alpha)');
+xlim([-5 15]);
+grid on;
\ No newline at end of file
diff --git a/TFGChang/NavierStokesProblemSolver.m b/TFGChang/NavierStokesProblemSolver.m
new file mode 100644
index 0000000000..a47bf70aa0
--- /dev/null
+++ b/TFGChang/NavierStokesProblemSolver.m
@@ -0,0 +1,347 @@
+classdef NavierStokesProblemSolver < handle
+
+    properties (Access = public)
+        velocityFun
+        pressureFun
+    end
+
+    properties (Access = private)
+        mesh
+        forcesFormula
+        dirConditions
+        dirDofs
+        material
+        velocityField
+        nu
+        dt
+    end
+
+    properties (Access = private)
+        diffTime
+        numDofs
+        solver
+        LHSS
+        LHS
+        RHS
+        x
+        fullX
+        u
+        p
+        M
+        D
+        KU
+        KP
+        C
+        uT
+    end
+
+    methods (Access = public)
+
+        function obj = NavierStokesProblemSolver(cParams)
+            obj.init(cParams);
+            obj.setDiffTime();
+            obj.calculateNumDofs();
+            obj.createSolver();
+        end
+
+        function compute(obj)
+            obj.solveNVProblem();
+        end
+
+    end
+
+    methods (Access = private)
+
+        function init(obj,cParams)
+            obj.mesh             = cParams.mesh;
+            obj.velocityFun      = cParams.velocityFun;
+            obj.pressureFun      = cParams.pressureFun;
+            obj.forcesFormula    = cParams.forcesFormula;
+            obj.dirConditions    = cParams.dirConditions;
+            obj.dirDofs          = cParams.dirDofs;
+            obj.material         = cParams.material;
+            obj.velocityField    = cParams.velocityField;
+            obj.nu               = cParams.nu;
+            obj.dt               = cParams.dt;
+        end
+
+        function setDiffTime(obj)
+            obj.diffTime = Inf;
+        end
+
+        function calculateNumDofs(obj)
+            obj.numDofs = obj.velocityFun.nDofs + obj.pressureFun.nDofs;
+        end
+
+        function createSolver(obj)
+            b.type =  'DIRECT';
+            obj.solver = Solver.create(b);
+        end
+
+        function computeLHSStokes(obj)
+            c.type          = 'Stokes';
+            c.dt            = obj.diffTime;
+            c.mesh          = obj.mesh;
+            c.material      = obj.material;
+            c.velocityFun   = obj.velocityFun;
+            c.pressureFun   = obj.pressureFun;
+            LHSintegratorg  = LHSIntegrator.create(c);
+            obj.LHS         = LHSintegratorg.compute();
+            obj.LHSS        = obj.LHS;
+        end
+
+        function computeLHSNS(obj,residual)
+            c.type          = 'NavierStokes';
+            c.mesh          = obj.mesh;
+            c.material      = obj.material;
+            c.velocityField = obj.velocityField;
+            c.velocityFun   = obj.velocityFun;
+            c.pressureFun   = obj.pressureFun;
+            c.LHSS          = obj.LHSS;
+            c.dt            = obj.dt;
+            c.residual      = residual;
+            LHSintegratorg  = LHSIntegrator.create(c);
+            obj.LHS         = LHSintegratorg.compute();
+        end
+
+        function computeLHSMatrixNS(obj)
+            c.type                          = 'NavierStokes';
+            c.mesh                          = obj.mesh;
+            c.material                      = obj.material;
+            c.velocityField                 = obj.velocityField;
+            c.velocityFun                   = obj.velocityFun;
+            c.pressureFun                   = obj.pressureFun;
+            c.dt                            = obj.dt;
+            LHSintegratorg                  = LHSIntegrator.create(c);
+            [obj.M, obj.D, obj.KU, obj.KP]  = LHSintegratorg.computeLHSMatrix();
+        end
+
+        function computeLHSConvectiveMatrix(obj)
+            c.type          = 'NavierStokes';
+            c.mesh          = obj.mesh;
+            c.material      = obj.material;
+            c.velocityField = obj.velocityField;
+            c.velocityFun   = obj.velocityFun;
+            c.dt            = obj.dt;
+            LHSintegratorg  = LHSIntegrator.create(c);
+            obj.C           = LHSintegratorg.computeConvectiveTerm();
+        end
+
+        function computeTentativeVelocity(obj)
+            uN  = obj.velocityField.fValues;
+            uN  = reshape(uN.', [], 1);
+            LHSTV   = obj.M + obj.C + obj.KU;
+            RHSTV   = obj.M * uN;
+            obj.uT  = obj.solver.solve(LHSTV, RHSTV);
+        end
+
+        function computePressure(obj)
+            RHSP     = obj.D * obj.uT ./ obj.dt;
+            obj.p    = obj.solver.solve(obj.KP,RHSP);
+        end
+
+        function computeVelocity(obj)
+            obj.u = obj.uT - obj.dt * obj.D * obj.p;
+        end
+
+        function computeRHS(obj)
+            d.type          = 'Stokes';
+            d.mesh          = obj.mesh;
+            d.velocityFun   = obj.velocityFun;
+            d.pressureFun   = obj.pressureFun;
+            d.forcesFormula = obj.forcesFormula;
+            RHSint          = RHSIntegrator.create(d);
+            F               = RHSint.integrate();
+            uD      = obj.dirConditions(:,3);
+            R       = -obj.LHS(:,obj.dirDofs)*uD;
+            obj.RHS = F + R;
+        end
+
+        function computeSolution(obj)
+            freeDofsPlus = setdiff(1:obj.numDofs,obj.dirDofs);
+            LHSr         = obj.LHS(freeDofsPlus,freeDofsPlus);
+            RHSr         = obj.RHS(freeDofsPlus);
+            obj.x        = obj.solver.solve(LHSr, RHSr);
+        end
+
+        function addDirBoundaryConditions(obj)
+            uD                 = obj.dirConditions(:,3);
+            nSteps             = length(obj.x(1,:));
+            uD                 = repmat(uD,1,nSteps);
+            obj.fullX          = zeros(obj.numDofs,nSteps);
+            freeDofs           = setdiff(1:(obj.numDofs),obj.dirDofs);
+            obj.fullX(freeDofs,:) = obj.x;
+            if ~isempty(obj.dirDofs)
+                obj.fullX(obj.dirDofs,:) = uD;
+            end
+        end
+
+        function addDirBCToVelocity(obj)
+            uD                 = obj.dirConditions(1:end - 1,3);
+            uDirDofs           = obj.dirDofs(1:end - 1);
+            if ~isempty(uDirDofs)
+                obj.u(uDirDofs,:) = uD;
+            end
+        end
+
+        function addDirBCToPressure(obj)
+            pD                 = obj.dirConditions(end,3);
+            pDirDofs           = obj.dirDofs(end);
+            if ~isempty(pDirDofs)
+                obj.p(pDirDofs,:) = pD;
+            end
+        end
+
+        function separateVariables(obj)
+            ndofsV = obj.velocityFun.nDofs;
+            obj.u = obj.fullX(1:ndofsV,:);
+            obj.p = obj.fullX(ndofsV+1:end,:);
+        end
+
+        function defineVariablesFValues(obj)
+            nFieldu = obj.velocityFun.ndimf;
+            nnode   = round(length(obj.u)/nFieldu);
+            nodes   = 1:nnode;
+            velfval = zeros(nnode,nFieldu);
+            for idim = 1:nFieldu
+                dofs = nFieldu*(nodes-1)+idim;
+                velfval(:,idim) = obj.u(dofs, end);
+            end
+            obj.velocityFun.setFValues(velfval);
+            obj.pressureFun.setFValues(obj.p(:,end));
+        end
+
+        function initPicardIteration(obj)
+            obj.computeLHSStokes();
+            %obj.computeLHSMatrixNS();
+            %obj.computeLHSNS();
+            obj.computeRHS();
+            obj.computeSolution();
+            obj.addDirBoundaryConditions();
+            obj.separateVariables();
+            obj.defineVariablesFValues();
+        end
+
+        function initPicardIterationFSM(obj)
+            obj.computeLHSStokes();
+            obj.computeLHSMatrixNS();
+            %obj.computeLHSNS();
+            obj.computeRHS();
+            obj.computeSolution();
+            obj.addDirBoundaryConditions();
+            obj.separateVariables();
+            obj.defineVariablesFValues();
+        end
+
+        function computePicardIteration(obj,residual)
+            obj.computeLHSNS(residual);
+            %obj.computeLHSMatrixNS();
+            obj.computeRHS();
+            obj.computeSolution();
+            obj.addDirBoundaryConditions();
+            obj.separateVariables();
+            obj.defineVariablesFValues();
+        end
+
+        function [Residual, ReError] = computeError(obj)
+            vNew = obj.velocityFun.fValues;
+            vOld = obj.velocityField.fValues;
+            denom = max(abs(vNew), 1e-12);
+
+            Residual = max(max(abs(vNew - vOld)));
+            ReError  = max(max(abs((vNew - vOld) ./ denom)));
+        end
+
+        function solveNVProblemFSM(obj)
+
+            Residual     = 1;
+            ReError      = 1;
+            iter         = 1;
+            maxIter      = 1e3;
+            tolRes       = 1e-6;
+            tolReE       = 1e-4;
+
+            if obj.nu < 1e-3
+                relaxFactor = 0.5;
+            elseif obj.nu < 1e-2
+                relaxFactor = 0.7;
+            else
+                relaxFactor = 1;
+            end
+
+            obj.initPicardIterationFSM()
+
+            fprintf('   Picard Iteration             Residual                ReError\n');
+
+            while ~((Residual <= tolRes && ReError <= tolReE) || iter >= maxIter)
+
+                obj.computeLHSConvectiveMatrix();
+                obj.computeTentativeVelocity();
+                obj.computePressure();
+                obj.computeVelocity();
+
+                obj.addDirBCToVelocity();
+                obj.defineVariablesFValues();
+
+                [Residual, ReError] = obj.computeError();
+
+                fprintf(['      %d               ' ...
+                    '        %.7e          %.5e\n'], iter, Residual, ReError);
+
+                relaxedVel = (1 - relaxFactor) * obj.velocityField.fValues + relaxFactor * obj.velocityFun.fValues;
+                obj.velocityField.setFValues(relaxedVel);
+
+                iter = iter + 1;
+
+            end
+
+        end
+
+        function solveNVProblem(obj)
+
+            Residual     = 1;
+            ReError      = 1;
+            iter         = 1;
+            maxIter      = 1e3;
+            tolRes       = 1e-6;
+            tolReE       = 1e-4;
+
+            if obj.nu < 1e-3
+                relaxFactor = 0.5;
+            elseif obj.nu < 1e-2
+                relaxFactor = 0.7;
+            else
+                relaxFactor = 1;
+            end
+
+            if all(obj.velocityField.fValues(:) == 0)
+                obj.initPicardIteration();
+                obj.velocityField.setFValues(obj.velocityFun.fValues);
+            else
+
+                obj.computeLHSStokes()
+            end
+            fprintf('   Picard Iteration             Residual                ReError\n');
+
+            while ~((Residual <= tolRes && ReError <= tolReE) || iter >= maxIter)
+
+                obj.computePicardIteration(Residual);
+
+                [Residual, ReError] = obj.computeError();
+
+                fprintf(['      %d               ' ...
+                    '        %.7e          %.5e\n'], iter, Residual, ReError);
+
+                relaxedVel = (1 - relaxFactor) * obj.velocityField.fValues + relaxFactor * obj.velocityFun.fValues;
+                obj.velocityField.setFValues(relaxedVel);
+
+                iter = iter + 1;
+
+            end
+
+        end
+
+
+    end
+
+end
\ No newline at end of file
diff --git a/TFGChang/StokesNetwork.m b/TFGChang/StokesNetwork.m
new file mode 100644
index 0000000000..31d3df1b1c
--- /dev/null
+++ b/TFGChang/StokesNetwork.m
@@ -0,0 +1,248 @@
+clc;
+clear;
+close all;
+
+%% Preprocess and Save Dataset
+
+OriginalData = readmatrix('E_AoA5_mpt.txt');
+data         = Data.preProcessDataset(OriginalData);
+
+save("EAoA5Datas.mat","data");
+
+%% Initialize and Train the NN
+
+for i = 1:1:1
+
+    % Store dataset file name
+    s.fileName          = "EDatasNS.mat";
+    s.testRatio         = 20;
+    s.k                 = i;
+    s.polynomialOrder   = 1;
+
+    % Select the model's features
+    s.xFeatures = [1, 2, 3, 4];
+    s.yFeatures = 7;
+
+    % Load data
+    data   = Data(s);
+    s.data = data;
+
+    % Initialization
+
+    % Load model parameters
+    s.networkParams.hiddenLayers    = s.polynomialOrder * size(s.xFeatures,2)* 9 * ones(1,6);
+    s.optimizerParams.learningRate  = 0.05;
+    s.costParams.lambda             = 0;
+    s.costParams.costType           = 'L2';
+
+    s.networkParams.HUtype = 'ReLU';
+    s.networkParams.OUtype = 'linear';
+
+    % Train the model
+    opt = OptimizationProblem(s);
+    opt.solve();
+    opt.plotCostFnc();
+
+    % Compute Error
+
+    MSETrain(i)    = immse(opt.computeOutputValues(data.Xtrain), data.Ytrain);
+    MSETest(i)     = immse(opt.computeOutputValues(data.Xtest), data.Ytest);
+
+    disp("MSE:")
+    disp(MSETrain)
+    disp(MSETest)
+
+end
+
+% Compute Mean Error
+
+disp("------")
+disp(mean(MSETrain));
+disp(mean(MSETest));
+
+%% Init for Plot
+
+dataset  = readmatrix("E_AoA5_mpt.txt");
+
+normalized = true;
+if (normalized == true)
+    load("StokesNN.mat");
+    EData = readmatrix("EData.txt");
+    maxValue        = max(EData(:,end));
+    minValue        = min(EData(:,end));
+    dataset(:,end)  = (dataset(:,end) - minValue) / (maxValue - minValue);
+else
+    load("StokesNNO.mat")
+end
+
+%% Plot Symmetric Airfoil E Data Comparison
+
+yDataSym = opt.computeOutputValues(dataset(1:16, 1:4));
+
+% Extract Original Data
+tSym = dataset(1:16,3);
+eSym = dataset(1:16,end);
+
+figure;
+plot(tSym, eSym);
+hold on;
+plot(tSym, yDataSym);
+legend('Location', 'best');
+title("Aerodynamic efficiency of symmetric airfoil vs thickness (t) - AoA 5º");
+xlabel('Thickness (t)');
+ylabel('Aerodynamic Efficiency');
+legend('Ground Truth', 'Predicted');
+
+figure;
+ReError = (yDataSym - eSym) ./  eSym;
+plot(tSym, ReError);
+title("Relative Error between Ground Truth and Predicted Aerodynamic Efficiency of Symmetric Airfoil vs Thickness (t)");
+xlabel('Thickness (t)');
+ylabel('Relative Error');
+
+%% Plot Asymetric Airfoil E Surface
+
+% Extract Original Data
+mT = dataset(17:end,1);
+pT = dataset(17:end,2);
+tT = dataset(17:end,3);
+eT = dataset(17:end,end);
+
+m = unique(mT);
+p = unique(pT);
+
+[M,P] = meshgrid(m,p);
+
+% Thickness Values to Plot
+thicknesses = [0.1, 0.2, 0.3, 0.4];
+
+figure;
+
+for i = 1:length(thicknesses)
+    ti = thicknesses(i);
+
+    idx = abs(tT - ti) < 1e-3;
+
+    if (i == 1)
+        mi = mT(idx);
+        pi = pT(idx);
+    end
+
+    ei = eT(idx);
+
+    F = scatteredInterpolant(mi, pi, ei, 'linear', 'none');
+    E(:,:,i) = F(M, P);
+
+    subplot(2, 2, i);
+    surface(M,P,E(:,:,i));
+    shading interp;
+    title(sprintf('t = %.2f', ti));
+    xlabel('Max Camber (m)');
+    ylabel('Max Camber Position (p)');
+    axis tight;
+    colorbar;
+end
+
+sgtitle('Ground truth aerodynamic efficiency (E) vs. m and p for different thickness (t) - AoA 5º','FontWeight', 'bold');
+
+% Compute Predicted Outputs y
+
+yData = opt.computeOutputValues(dataset(17:end, 1:4));
+figure;
+
+for i = 1:length(thicknesses)
+    ti = thicknesses(i);
+
+    idx = abs(tT - ti) < 1e-3;
+    ei = yData(idx);
+
+    F = scatteredInterpolant(mi, pi, ei, 'linear', 'none');
+    EP(:,:,i) = F(M, P);
+
+    subplot(2, 2, i);
+    surface(M,P,EP(:,:,i));
+    shading interp;
+    title(sprintf('t = %.2f', ti));
+    xlabel('Max Camber (m)');
+    ylabel('Max Camber Position (p)');
+    axis tight;
+    colorbar;
+end
+
+sgtitle('Predicted aerodynamic efficiency vs. m and p for different thickness (t) - AoA 5º','FontWeight', 'bold');
+
+ReError = abs(EP - E) ./ E;
+
+figure;
+
+for i = 1:length(thicknesses)
+    ti = thicknesses(i);
+
+    subplot(2, 2, i);
+    surface(M,P,ReError(:,:,i));
+    shading interp;
+    title(sprintf('t = %.2f', ti));
+    xlabel('Max Camber (m)');
+    ylabel('Max Camber Position (p)');
+    axis tight;
+    colorbar;
+end
+
+sgtitle('Relative error between prediction and ground truth vs. m and p for different thickness (t) - AoA 5º','FontWeight', 'bold');
+
+%% Plot Merged E Surface
+
+% Compute Predicted Outputs
+yData  = opt.computeOutputValues(dataset(17:end, 1:4));
+
+% Extract Original Data
+mT = dataset(17:end,1);
+pT = dataset(17:end,2);
+tT = dataset(17:end,3);
+eT = dataset(17:end,end);
+
+m = unique(mT);
+p = unique(pT);
+
+[M,P] = meshgrid(m,p);
+
+% Thickness Values to Plot
+thicknesses = [0.1, 0.2, 0.3, 0.4];
+
+figure;
+
+for i = 1:length(thicknesses)
+    ti = thicknesses(i);
+
+    idx = abs(tT - ti) < 1e-3;
+
+    if (i == 1)
+        mi = mT(idx);
+        pi = pT(idx);
+    end
+
+    eiT = eT(idx);
+    eiP = yData(idx);
+
+    F = scatteredInterpolant(mi, pi, eiT, 'linear', 'none');
+    E(:,:,i) = F(M, P);
+
+    F = scatteredInterpolant(mi, pi, eiP, 'linear', 'none');
+    EP(:,:,i) = F(M, P);
+
+    subplot(2, 2, i);
+    surface(M,P,E(:,:,i),'FaceColor', 'blue', 'EdgeColor', 'none', 'DisplayName', 'Ground Truth');
+    surface(M,P,EP(:,:,i),'FaceColor', [1, 0.5, 0], 'EdgeColor', 'none', 'DisplayName', 'Predicted');
+    alpha(0.7);
+    view(125,20)
+
+    legend('Location', 'best');
+    %shading interp;
+    title(sprintf('t = %.2f', ti));
+    xlabel('Max Camber (m)');
+    ylabel('Max Camber Position (p)');
+    axis tight;
+    %colorbar;
+end
+
+sgtitle('Ground truth and predicted efficiency vs. m and p for different thickness (t)','FontWeight', 'bold');
diff --git a/TFGChang/StokesOptimization.m b/TFGChang/StokesOptimization.m
new file mode 100644
index 0000000000..548551fa52
--- /dev/null
+++ b/TFGChang/StokesOptimization.m
@@ -0,0 +1,44 @@
+% Stoke Problem Optimization
+% clc
+% clear;
+close all;
+
+% Read Network data
+load("StokesNN.mat");
+
+% Initialization
+m   = 0.09;
+p   = 0.8;
+t   = 0.4;
+AoA = 1;
+
+d.features      = [m,p,t,AoA];
+d.learningRate  = 0.5;
+d.optimizer     = opt;
+d.tol           = 1e-6;
+d.lowerBC = [0.0, 0.0, 0.1, -2.5];
+d.upperBC = [0.09, 0.9, 0.4, 15.0];
+
+% Compute the Optimization
+stokeOpt = AirfoilOptimizer(d);
+stokeOpt.computeOptAirfoilParams();close 
+
+% Results
+OptimalParams = stokeOpt.optimalParams;
+
+% Plot the Optimal Airfoil
+figure;
+AirfoilOptimizer.plotAirfoilContour(OptimalParams,0)
+
+%% Plot E vs iterations
+
+stokeOpt.plotEEvolution();
+
+%% Generate the Airfoil Shape Optimization Video
+
+stokeOpt.generateAFSOPVideo();
+ close all
+stokeOpt.generateVelVideo();
+ close all
+stokeOpt.generatePVideo();
+ close all
diff --git a/TFGChang/StokesProblemBoundaryCondition.m b/TFGChang/StokesProblemBoundaryCondition.m
new file mode 100644
index 0000000000..2faface54a
--- /dev/null
+++ b/TFGChang/StokesProblemBoundaryCondition.m
@@ -0,0 +1,186 @@
+classdef StokesProblemBoundaryCondition < handle
+    properties (Access = public)
+        dirConditions
+        dirDofs
+        nodesConditions
+    end
+
+    properties (Access = private)
+        height
+        mesh
+        uMesh
+        velocityFun
+        pressureFun
+    end
+
+    properties (Access = private)
+        isLeft
+        isRight
+        isBottom
+        isTop
+        isHorizontal
+        dirVelBC
+        dirPreBC
+        nnodesCutMesh
+        dirDofsAirfoilMNodes
+        middleNodesCoor
+        dirDofsAirfoilNodes
+        useMiddleNodes
+    end
+
+    methods (Access = public)
+        function obj = StokesProblemBoundaryCondition(cParams)
+            obj.init(cParams);
+            obj.defineVariables();
+            obj.defineDomainBoundaries();
+            obj.useMiddleNodes = strcmpi(obj.velocityFun.order, 'P2');
+        end
+
+        function compute(obj)
+            obj.setDomainDirichletVelocityBC();
+            obj.setDofsAirfoil();
+            obj.defineNodesConditions();
+            obj.constructDirichletVelBCMatrix();
+            obj.setDomainDirichletPressureBC();
+            obj.constructDirichletPressureBCMatrix();
+        end
+    end
+
+    methods (Access = private)
+        function init(obj, cParams)
+            obj.height      = cParams.height;
+            obj.mesh        = cParams.mesh;
+            obj.uMesh       = cParams.uMesh;
+            obj.velocityFun = cParams.velocityFun;
+            obj.pressureFun = cParams.pressureFun;
+        end
+
+        function defineVariables(obj)
+            obj.dirConditions = [];
+            obj.dirDofs       = [];
+            obj.nodesConditions = [];
+        end
+
+        function defineDomainBoundaries(obj)
+            tolerance = 1e-12;
+            obj.isLeft       = @(coor) (abs(coor(:,1) - min(coor(:,1))) < tolerance);
+            obj.isRight      = @(coor) (abs(coor(:,1) - max(coor(:,1))) < tolerance);
+            obj.isBottom     = @(coor) (abs(coor(:,2) - min(coor(:,2))) < tolerance);
+            obj.isTop        = @(coor) (abs(coor(:,2) - max(coor(:,2))) < tolerance);
+            obj.isHorizontal = @(coor) (abs(coor(:,2) - obj.height/2) < tolerance);
+        end
+
+        function setDomainDirichletVelocityBC(obj)
+            obj.dirVelBC{1}.domain    = @(coor) obj.isLeft(coor) & ~ (obj.isTop(coor) | obj.isBottom(coor));
+            obj.dirVelBC{1}.direction = [1, 2];
+            obj.dirVelBC{1}.value     = [1, 0];
+
+            obj.dirVelBC{2}.domain    = @(coor) obj.isTop(coor) | obj.isBottom(coor);
+            obj.dirVelBC{2}.direction = [1, 2];
+            obj.dirVelBC{2}.value     = [0, 0];
+        end
+
+        function setDofsAirfoilNodes(obj)
+            cutCoords = obj.uMesh.boundaryCutMesh.mesh.coord;
+            tol = 1e-10;
+            isAirfoil = @(coor) any(pdist2(coor, cutCoords) < tol, 2);
+            obj.dirDofsAirfoilNodes = obj.velocityFun.getDofsFromCondition(isAirfoil);
+            obj.dirDofsAirfoilNodes = sort(reshape(obj.dirDofsAirfoilNodes, [], 1));
+        end
+
+        function setAirfoilDirichletVelocityBC(obj)
+            cutCoords = obj.uMesh.boundaryCutMesh.mesh.coord;
+            ind = numel(obj.dirVelBC);
+            obj.dirVelBC{ind+1}.domain = @(coor) any(ismember(coor, cutCoords, 'rows'), 2);
+            obj.dirVelBC{ind+1}.direction = [1, 2];
+            obj.dirVelBC{ind+1}.value = [0, 0];
+        end
+
+        function findMiddleNodes(obj)
+            if ~obj.useMiddleNodes
+                obj.middleNodesCoor = [];
+                obj.dirVelBC{end+1}.value = [0, 0];
+                return
+            end
+            bCutMesh = obj.uMesh.boundaryCutMesh.mesh;
+            x1 = bCutMesh.coord(bCutMesh.connec(:,1), :);
+            x2 = bCutMesh.coord(bCutMesh.connec(:,2), :);
+            obj.middleNodesCoor = (x1 + x2) / 2;
+        end
+
+        function setDofsAirfoilMNodes(obj)
+            if ~obj.useMiddleNodes
+                obj.dirDofsAirfoilMNodes = [];
+                return
+            end
+            nEdges = size(obj.uMesh.boundaryCutMesh.mesh.connec, 1);
+            obj.dirDofsAirfoilMNodes = zeros(2, nEdges);
+            for i = 1:nEdges
+                isxcoord = @(coor) abs(coor(:,1) - obj.middleNodesCoor(i,1)) < 1e-12;
+                isycoord = @(coor) abs(coor(:,2) - obj.middleNodesCoor(i,2)) < 1e-12;
+                isAirfoil = @(coor) isxcoord(coor) & isycoord(coor);
+
+                obj.dirDofsAirfoilMNodes(:, i) = obj.velocityFun.getDofsFromCondition(isAirfoil);
+            end
+            obj.dirDofsAirfoilMNodes = sort(reshape(obj.dirDofsAirfoilMNodes, [], 1));
+            obj.dirVelBC{end+1}.value = [0, 0];
+        end
+
+        function setDofsAirfoil(obj)
+            obj.setDofsAirfoilNodes();
+            obj.setAirfoilDirichletVelocityBC();
+            obj.findMiddleNodes();
+            obj.setDofsAirfoilMNodes();
+        end
+
+        function defineNodesConditions(obj)
+            obj.nodesConditions = 1 + (obj.dirDofsAirfoilNodes(2:2:end)-2)/obj.velocityFun.ndimf;
+        end
+
+        function constructDirichletVelBCMatrix(obj)
+            n = numel(obj.dirVelBC);
+            for i = 1:n
+                if i < n-1
+                    dirDofsVel = obj.velocityFun.getDofsFromCondition(obj.dirVelBC{i}.domain);
+                elseif i == n-1
+                    dirDofsVel = obj.dirDofsAirfoilNodes;
+                else
+                    if ~isempty(obj.dirDofsAirfoilMNodes)
+                        dirDofsVel = obj.dirDofsAirfoilMNodes;
+                    else
+
+                        continue;
+                    end
+                end
+
+                nodes = 1 + (dirDofsVel(2:2:end)-2)/obj.velocityFun.ndimf;
+                nodesDuplicated = repmat(nodes, [1 2]);
+                sortedNodes = sort(nodesDuplicated(:));
+                direction = repmat([1; 2], [length(sortedNodes)/2 1]);
+                value = repmat(obj.dirVelBC{i}.value', [length(sortedNodes)/2 1]);
+
+                obj.dirConditions = [obj.dirConditions; [sortedNodes direction value]];
+                obj.dirDofs = [obj.dirDofs; dirDofsVel];
+            end
+        end
+
+
+        function setDomainDirichletPressureBC(obj)
+            obj.dirPreBC{1}.domain = @(coor) obj.isRight(coor);
+            obj.dirPreBC{1}.direction = 1;
+            obj.dirPreBC{1}.value = 0;
+        end
+
+        function constructDirichletPressureBCMatrix(obj)
+            for i = 1:length(obj.dirPreBC)
+                dirDofsPre = obj.pressureFun.getDofsFromCondition(obj.dirPreBC{i}.domain);
+                dirDofsPre = dirDofsPre(ceil(length(dirDofsPre)/2));
+                direction = ones(size(dirDofsPre));
+                value = ones(size(dirDofsPre)) * obj.dirPreBC{i}.value;
+                obj.dirConditions(end+1:end+length(dirDofsPre), :) = [dirDofsPre + obj.velocityFun.nDofs direction value];
+                obj.dirDofs(end+1:end+length(dirDofsPre), 1) = dirDofsPre + obj.velocityFun.nDofs;
+            end
+        end
+
+    end
+end
diff --git a/TFGChang/StokesProblemSolver.m b/TFGChang/StokesProblemSolver.m
new file mode 100644
index 0000000000..77581dbc9f
--- /dev/null
+++ b/TFGChang/StokesProblemSolver.m
@@ -0,0 +1,138 @@
+classdef StokesProblemSolver < handle
+
+    properties (Access = public)
+        velocityFun
+        pressureFun
+    end
+
+    properties (Access = private)
+        mesh
+        forcesFormula
+        dirConditions
+        dirDofs
+        material
+    end
+
+    properties (Access = private)
+        diffTime
+        numDofs
+        solver
+        LHS
+        RHS
+        x
+        fullX
+        u
+        p
+    end
+
+    methods (Access = public)
+
+        function obj = StokesProblemSolver(cParams)
+            obj.init(cParams);
+            obj.setDiffTime();
+            obj.calculateNumDofs();
+            obj.createSolver();
+        end
+
+        function compute(obj)
+            obj.computeLHS();
+            obj.computeRHS();
+            obj.solveProblem();
+            obj.addDirBoundaryConditions();
+            obj.separateVariablesFvalues();
+            obj.defineVariables();
+        end
+
+    end
+
+    methods (Access = private)
+
+        function init(obj,cParams)
+            obj.mesh             = cParams.mesh;
+            obj.velocityFun      = cParams.velocityFun;
+            obj.pressureFun      = cParams.pressureFun;
+            obj.forcesFormula    = cParams.forcesFormula;
+            obj.dirConditions    = cParams.dirConditions;
+            obj.dirDofs          = cParams.dirDofs;
+            obj.material         = cParams.material;
+        end
+
+        function setDiffTime(obj)
+            obj.diffTime = Inf;
+        end
+
+        function calculateNumDofs(obj)
+            obj.numDofs = obj.velocityFun.nDofs + obj.pressureFun.nDofs;
+        end
+
+        function createSolver(obj)
+            b.type =  'DIRECT';
+            obj.solver = Solver.create(b);
+        end
+
+        function computeLHS(obj)
+            c.type          = 'Stokes';
+            c.dt            = obj.diffTime;
+            c.mesh          = obj.mesh;
+            c.material      = obj.material;
+            c.velocityFun   = obj.velocityFun;
+            c.pressureFun   = obj.pressureFun;
+            LHSintegratorg  = LHSIntegrator.create(c);
+            obj.LHS         = LHSintegratorg.compute();
+        end
+
+        function computeRHS(obj)
+            d.type          = 'Stokes';
+            d.mesh          = obj.mesh;
+            d.velocityFun   = obj.velocityFun;
+            d.pressureFun   = obj.pressureFun;
+            d.forcesFormula = obj.forcesFormula;
+            RHSint          = RHSIntegrator.create(d);
+            F               = RHSint.integrate();
+            uD      = obj.dirConditions(:,3);
+            R       = -obj.LHS(:,obj.dirDofs)*uD;
+            obj.RHS = F + R;
+        end
+
+        function solveProblem(obj)
+            freeDofsPlus = setdiff(1:obj.numDofs,obj.dirDofs);
+            LHSr         = obj.LHS(freeDofsPlus,freeDofsPlus);
+            RHSr         = obj.RHS(freeDofsPlus);
+            obj.x        = obj.solver.solve(LHSr, RHSr);
+        end
+
+        function addDirBoundaryConditions(obj)
+            uD                 = obj.dirConditions(:,3);
+            nSteps             = length(obj.x(1,:));
+            uD                 = repmat(uD,1,nSteps);
+            obj.fullX          = zeros(obj.numDofs,nSteps);
+            freeDofs           = setdiff(1:(obj.numDofs),obj.dirDofs);
+            obj.fullX(freeDofs,:) = obj.x;
+            if ~isempty(obj.dirDofs)
+                obj.fullX(obj.dirDofs,:) = uD;
+            end
+        end
+
+        function separateVariablesFvalues(obj)
+            ndofsV = obj.velocityFun.nDofs;
+            obj.u = obj.fullX(1:ndofsV,:);
+            obj.p = obj.fullX(ndofsV+1:end,:);
+        end
+
+        function defineVariables(obj)
+            nFieldu = obj.velocityFun.ndimf;
+            nnode   = round(length(obj.u)/nFieldu);
+            nodes   = 1:nnode;
+            velfval = zeros(nnode,nFieldu);
+            for idim = 1:nFieldu
+                dofs = nFieldu*(nodes-1)+idim;
+                velfval(:,idim) = obj.u(dofs, end);
+            end
+            obj.velocityFun.setFValues(velfval);
+            obj.pressureFun.setFValues(obj.p(:,end));
+        end
+
+
+    end
+
+end
\ No newline at end of file
diff --git a/TFGChang/TestNaca.m b/TFGChang/TestNaca.m
new file mode 100644
index 0000000000..c16af60843
--- /dev/null
+++ b/TFGChang/TestNaca.m
@@ -0,0 +1,384 @@
+classdef TestNaca < handle
+
+    properties (Access = public)
+        L
+        D
+        E
+        velocityFun
+        pressureFun
+        convectVel
+    end
+
+    properties (Access = private)
+        M
+        p
+        t
+        AoA
+        chord
+        length
+        height
+        nx
+        ny
+        flowType
+        nu
+        i
+    end
+
+    properties (Access = private)
+        refMesh
+        levelSet
+        rawMesh
+        mesh
+        backupmesh
+        uMesh
+        material
+        filter
+        forcesFormula
+        dirConditions
+        dirDofs
+        nodesConditions
+        velocityField
+    end
+
+    methods (Access = public)
+
+        function obj = TestNaca(cParams)
+            %close all;
+            obj.init(cParams);
+            obj.createReferenceMesh();
+            [AirfoilParams, BGParams] = obj.setParams();
+            obj.createLevelSet(AirfoilParams, BGParams);
+            obj.createFluidMesh();
+            %obj.plotMesh();
+            %obj.createFluidMeshGoodConditioning(AirfoilParams, BGParams));
+            obj.createMaterial();
+            obj.createTrialFunction();
+            obj.defineBoundaryConditions();
+            obj.defineAppliedForces();
+        end
+
+        function compute(obj)
+            obj.createPressureFilter();
+            obj.solveProblem();
+            obj.CalculateAeroForces();
+        end
+
+        function validate(obj)
+            obj.verifyAeroForces();
+        end
+
+        function print(obj)
+            obj.printResults();
+        end
+
+    end
+
+    methods (Access = private)
+
+        function init(obj,cParams)
+            obj.p        = cParams.p;
+            obj.M        = cParams.M;
+            obj.t        = cParams.t;
+            obj.AoA      = cParams.AoA;
+            obj.chord    = cParams.chord;
+            obj.length   = cParams.length;
+            obj.height   = cParams.height;
+            obj.nx       = cParams.nx;
+            obj.flowType = cParams.flowType;
+            if (obj.flowType == "NavierStokes")
+                obj.initNV(cParams);
+            end
+
+        end
+
+        function initNV(obj,cParams)
+            obj.nu          = cParams.nu;
+            obj.convectVel  = cParams.convectVel;
+        end
+
+        function [AirfoilParams, BGParams] = setParams(obj)
+            AirfoilParams.p      = obj.p;
+            AirfoilParams.M      = obj.M;
+            AirfoilParams.t      = obj.t;
+            AirfoilParams.AoA    = obj.AoA;
+            AirfoilParams.chord  = obj.chord;
+            BGParams.length      = obj.length;
+            BGParams.height      = obj.height;
+            BGParams.nx          = obj.nx;
+        end
+
+        function createReferenceMesh(obj)
+            obj.ny      = round(obj.nx / obj.length * obj.height / 0.8);
+            obj.refMesh = TriangleMesh(obj.length,obj.height,obj.nx,obj.ny);
+        end
+
+        function createLevelSet(obj,AirfoilParams, BGParams)
+            g = obj.createNacaFunction(AirfoilParams, BGParams);
+            obj.levelSet = g.computeLevelSetFunction(obj.refMesh);
+            %obj.levelSet.plot();
+        end
+
+        function createFluidMesh(obj)
+            s.backgroundMesh = obj.refMesh;
+            s.boundaryMesh   = obj.refMesh.createBoundaryMesh();
+            obj.uMesh        = UnfittedMesh(s);
+            obj.uMesh.compute(obj.levelSet.fValues);
+            obj.rawMesh = obj.uMesh.createInnerMesh();
+            obj.mesh    = obj.rawMesh;
+        end
+
+        function plotMesh(obj)
+            figure;
+            obj.mesh.plot();
+            title("Mesh with the airfoil inclusion.");
+            xlabel("x");
+            ylabel("y");
+        end
+
+        function createFluidMeshGoodConditioning(obj,AirfoilParams, BGParams)
+            m              = obj.createMeshAlphaTriangulation();
+            s.connec       = obj.computeConnectivitiesGoodCond(m,AirfoilParams, BGParams);
+            s.coord        = obj.rawMesh.coord;
+            m2             = Mesh.create(s);
+            obj.backupmesh = m2.computeCanonicalMesh();
+        end
+
+        function m = createMeshAlphaTriangulation(obj)
+            points = obj.rawMesh.coord;
+            r      = obj.computeAlphaDistance();
+            T      = alphaShape(points,r);
+            DT     = alphaTriangulation(T);
+
+            s.connec = DT;
+            s.coord  = points;
+            m        = Mesh.create(s);
+        end
+
+        function r = computeAlphaDistance(obj)
+            bCMesh = obj.uMesh.boundaryCutMesh.mesh;
+            x      = bCMesh.coord(:,1);
+            y      = bCMesh.coord(:,2);
+            xMax   = max(x);
+            xMin   = min(x);
+            yMax   = max(y);
+            yMin   = min(y);
+            r      = 0.25*min(xMax-xMin,yMax-yMin);
+            h      = obj.refMesh.computeMeanCellSize();
+            if h>=r
+                warning('Alpha radius is too small');
+            end
+        end
+
+        function connec = computeConnectivitiesGoodCond(obj,mAlpha,AirfoilParams, BGParams)
+            q        = Quadrature.create(mAlpha, 0);
+            xV       = q.posgp;
+            g  = obj.createNacaFunction(AirfoilParams, BGParams);
+            lsElem = squeeze(g.evaluate(xV,mAlpha));
+            connec = mAlpha.connec(lsElem<=0,:);
+        end
+
+        function createMaterial(obj)
+            e.type       = obj.flowType;
+            e.nelem      = obj.mesh.nelem;
+            e.nu         = obj.nu;
+            obj.material = Material.create(e);
+        end
+
+        function createTrialFunction(obj)
+
+            obj.pressureFun = LagrangianFunction.create(obj.mesh, 1, 'P1');
+
+            switch obj.flowType
+                case 'Stokes'
+                    obj.velocityFun = LagrangianFunction.create(obj.mesh, 2, 'P2');
+                case 'NavierStokes'
+                    obj.velocityFun    = LagrangianFunction.create(obj.mesh, 2, 'P2');
+                    obj.velocityField  = LagrangianFunction.create(obj.mesh, 2, 'P2');
+                    if ~isempty(obj.convectVel)
+                        obj.velocityField.setFValues(obj.convectVel);
+                    end
+                otherwise
+                    error('Unknown flow type: %s', obj.flowType);
+            end
+        end
+
+        function defineBoundaryConditions(obj)
+            s.height       = obj.height;
+            s.mesh         = obj.mesh;
+            s.uMesh        = obj.uMesh;
+            s.velocityFun  = obj.velocityFun;
+            s.pressureFun  = obj.pressureFun;
+            BCClass              = StokesProblemBoundaryCondition(s);
+            BCClass.compute();
+            obj.dirConditions    = BCClass.dirConditions;
+            obj.dirDofs          = BCClass.dirDofs;
+            obj.nodesConditions  = BCClass.nodesConditions;
+        end
+
+        function defineAppliedForces(obj)
+            sAF.fHandle       = @(coor) [0.*coor,0.*coor];
+            sAF.ndimf         = 2;
+            sAF.mesh          = obj.mesh;
+            obj.forcesFormula = AnalyticalFunction(sAF);
+        end
+
+        function createPressureFilter(obj)
+            s.filterType = 'PDE';
+            s.mesh       = obj.mesh;
+            s.trial      = obj.pressureFun;
+            obj.filter   = Filter.create(s);
+        end
+
+        function s = initProblemSolver(obj)
+            s.mesh             = obj.mesh;
+            s.forcesFormula    = obj.forcesFormula;
+            s.dirConditions    = obj.dirConditions;
+            s.dirDofs          = obj.dirDofs;
+            s.material         = obj.material;
+            s.velocityFun      = obj.velocityFun;
+            s.pressureFun      = obj.pressureFun;
+        end
+
+        function solveProblem(obj)
+            s = obj.initProblemSolver();
+
+            switch obj.flowType
+                case 'Stokes'
+                    obj.solveStokesProblem(s);
+                case 'NavierStokes'
+                    obj.solveNavierStokesProblem(s);
+                otherwise
+                    error('Unknown flow type: %s', obj.flowType);
+            end
+
+            obj.pressureFun = obj.filter.compute(obj.pressureFun, 3);
+
+        end
+
+        function solveStokesProblem(obj,s)
+            SolverResults      = StokesProblemSolver(s);
+            SolverResults.compute();
+            obj.velocityFun    = SolverResults.velocityFun;
+            obj.pressureFun    = SolverResults.pressureFun;
+        end
+
+        function solveNavierStokesProblem(obj,s)
+            s.nu             = obj.nu;
+            s.dt             = inf;
+            s.velocityField  = obj.velocityField;
+            SolverResults      = NavierStokesProblemSolver(s);
+            SolverResults.compute();
+            obj.velocityFun    = SolverResults.velocityFun;
+            obj.pressureFun    = SolverResults.pressureFun;
+        end
+
+        function plotResults(obj)
+            TestNaca.plotVelocity(obj.velocityFun);
+            TestNaca.plotVelocityX(obj.velocityFun);
+            TestNaca.plotVelocityY(obj.velocityFun);
+            TestNaca.plotPressure(obj.pressureFun);
+        end
+
+        function CalculateAeroForces(obj)
+            s.mesh             = obj.mesh;
+            s.nodesConditions  = obj.nodesConditions;
+            s.pressureFun      = obj.pressureFun;
+            AeroForcesResults  = AeroForcesCalculation(s);
+            AeroForcesResults.compute();
+            obj.L              = AeroForcesResults.L;
+            obj.D              = AeroForcesResults.D;
+            obj.E              = AeroForcesResults.E;
+        end
+
+        function verifyAeroForces(obj)
+            s.L    = obj.L;
+            s.D    = obj.D;
+            AeroForcesCalculationTest = AeroForcesCalculationTestComputer(s);
+            AeroForcesCalculationTest.compute();
+        end
+
+        function printResults(obj)
+            fileID = fopen('results.txt', 'a');
+            fprintf(fileID, '%.2f %.2f %.2f %.2f %.4e %.4e %.4f\n', obj.M, obj.p, obj.t, obj.AoA, obj.L, obj.D, obj.E);
+            fclose(fileID);
+        end
+
+
+    end
+
+    methods (Static, Access = public)
+
+        function plotVelocity(velocityFun)
+            v = LagrangianFunction.create(velocityFun.mesh, 1, 'P2');
+            v.setFValues(sqrt(velocityFun.fValues(:,1).^2 + velocityFun.fValues(:,2).^2));
+            v.plot()
+            title("Velocity distribution.");
+            xlabel("x");
+            ylabel("y");
+            colorbar;
+            axis image tight;
+            %set(gca, 'Position', [0.1 0.1 0.75 1]);
+            set(gcf, 'WindowState', 'maximized');
+        end
+
+        function plotVelocityX(velocityFun)
+            vx = LagrangianFunction.create(velocityFun.mesh, 1, 'P2');
+            vx.setFValues(velocityFun.fValues(:,1));
+            vx.plot();
+            title("Velocity distribution in the x direction.");
+            xlabel("x");
+            ylabel("y");
+            colorbar;
+            axis equal tight;
+            %set(gca, 'Position', [0.1 0 0.75 1]);
+            set(gcf, 'WindowState', 'maximized');
+        end
+
+        function plotVelocityY(velocityFun)
+            vy = LagrangianFunction.create(velocityFun.mesh, 1, 'P2');
+            vy.setFValues(velocityFun.fValues(:,2));
+            vy.plot();
+            title("Velocity distribution in the y direction.");
+            xlabel("x");
+            ylabel("y");
+            colorbar;
+            axis equal tight;
+            %set(gca, 'Position', [0.1 0 0.75 1]);
+            set(gcf, 'WindowState', 'maximized');
+        end
+
+        function plotPressure(PressureFun)
+            PressureFun.plot();
+            xlabel("x");
+            ylabel("y");
+            title("Pressure distribution");
+            axis equal tight;
+            colorbar;
+            caxis([-20, 20]);
+            %set(gca, 'Position', [0.1 0 0.75 1]);
+            set(gcf, 'WindowState', 'maximized');
+        end
+
+    end
+
+    methods (Static, Access = private)
+
+        function g = createNacaFunction(AirfoilParams, BGParams)
+            s.type = 'Naca'; % 'Naca
+            s.xLE  = (BGParams.length - AirfoilParams.chord) / 2;
+            s.yLE  = BGParams.height/2;
+
+            s.chord = AirfoilParams.chord;
+            s.p     = AirfoilParams.p;
+            s.m     = AirfoilParams.M;
+            s.t     = AirfoilParams.t;
+            s.AoA   = AirfoilParams.AoA;
+
+            g  = GeometricalFunction(s);
+        end
+
+    end
+
+
+
+end
\ No newline at end of file
diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/E_AOA0_nx600_PF_FL.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/E_AOA0_nx600_PF_FL.txt
new file mode 100644
index 0000000000..5b707e1a36
--- /dev/null
+++ b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/E_AOA0_nx600_PF_FL.txt
@@ -0,0 +1,70 @@
+0.00 0.20 0.12 0.00 0.0000 1.2051 0.0000
+0.00 0.30 0.12 0.00 0.0000 1.2051 0.0000
+0.00 0.40 0.12 0.00 0.0000 1.2051 0.0000
+0.00 0.50 0.12 0.00 0.0000 1.2051 0.0000
+0.00 0.60 0.12 0.00 0.0000 1.2051 0.0000
+0.00 0.70 0.12 0.00 0.0000 1.2051 0.0000
+0.00 0.80 0.12 0.00 0.0000 1.2051 0.0000
+0.01 0.20 0.12 0.00 0.0103 1.2166 0.0085
+0.01 0.30 0.12 0.00 0.0061 1.2158 0.0050
+0.01 0.40 0.12 0.00 0.0051 1.2159 0.0042
+0.01 0.50 0.12 0.00 0.0047 1.2172 0.0038
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/E_AOA0_nx600_PNF_FL.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/E_AOA0_nx600_PNF_FL.txt
new file mode 100644
index 0000000000..ed918312e4
--- /dev/null
+++ b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/E_AOA0_nx600_PNF_FL.txt
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/E_GF_N2412.mat b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/E_GF_N2412.mat
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index 0000000000..17587dbd9e
Binary files /dev/null and b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/E_GF_N2412.mat differ
diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/LD_N2412_AOA-+15_nx600_PF_FL.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/LD_N2412_AOA-+15_nx600_PF_FL.txt
new file mode 100644
index 0000000000..1bc479aed4
--- /dev/null
+++ b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/LD_N2412_AOA-+15_nx600_PF_FL.txt
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/LD_N2412_AOA-+15_nx600_PNF_FL.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/LD_N2412_AOA-+15_nx600_PNF_FL.txt
new file mode 100644
index 0000000000..0a941fe24b
--- /dev/null
+++ b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetFL/LD_N2412_AOA-+15_nx600_PNF_FL.txt
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetNFL_DEF/DatasN0010_AoA12-15.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetNFL_DEF/DatasN0010_AoA12-15.txt
new file mode 100644
index 0000000000..d7f9e82fb1
--- /dev/null
+++ b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetNFL_DEF/DatasN0010_AoA12-15.txt
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetNFL_DEF/LDE_NS_RE10.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetNFL_DEF/LDE_NS_RE10.txt
new file mode 100644
index 0000000000..c39364f390
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetNFL_DEF/LD_N2412_AoA-+15_nx420_PF_NFL.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetNFL_DEF/LD_N2412_AoA-+15_nx420_PF_NFL.txt
new file mode 100644
index 0000000000..88d88fbb68
--- /dev/null
+++ b/Tutorials/ShapeOptNetworkTutorial/Datasets/DatasetNFL_DEF/LD_N2412_AoA-+15_nx420_PF_NFL.txt
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/EA0A5DatasOS.mat b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/EA0A5DatasOS.mat
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index 0000000000..923d2eb33a
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/EDatasOS.mat b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/EDatasOS.mat
new file mode 100644
index 0000000000..bb36dabf2b
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA-2.5_mpt.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA-2.5_mpt.txt
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index 0000000000..edcd1787a8
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA0_mpt.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA0_mpt.txt
new file mode 100644
index 0000000000..d2ffa5b665
--- /dev/null
+++ b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA0_mpt.txt
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA10_mpt.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA10_mpt.txt
new file mode 100644
index 0000000000..dbfa850e60
--- /dev/null
+++ b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA10_mpt.txt
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA12.5_mpt.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA12.5_mpt.txt
new file mode 100644
index 0000000000..b4be584e88
--- /dev/null
+++ b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA12.5_mpt.txt
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA15_mpt.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA15_mpt.txt
new file mode 100644
index 0000000000..c95a5ce19f
--- /dev/null
+++ b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA15_mpt.txt
@@ -0,0 +1,1024 @@
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA2.5_mpt.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA2.5_mpt.txt
new file mode 100644
index 0000000000..44b962ac72
--- /dev/null
+++ b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA2.5_mpt.txt
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA5_mpt.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA5_mpt.txt
new file mode 100644
index 0000000000..1f4b195ddd
--- /dev/null
+++ b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA5_mpt.txt
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diff --git a/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA7.5_mpt.txt b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA7.5_mpt.txt
new file mode 100644
index 0000000000..87531089bf
--- /dev/null
+++ b/Tutorials/ShapeOptNetworkTutorial/Datasets/EDataset/E_AoA7.5_mpt.txt
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+0.09 0.80 0.40 7.50 1.0926 5.2934 0.2064
diff --git a/myMesh.flavia.msh b/myMesh.flavia.msh
deleted file mode 100644
index 0686e6bdff..0000000000
--- a/myMesh.flavia.msh
+++ /dev/null
@@ -1,17 +0,0 @@
-####################################################
-################# FEM-MAT-OO v.1.0 #################
-####################################################
-
-MESH "WORKPIECE" dimension   2   Elemtype Quadrilateral   Nnode  4 
- 
-coordinates 
-     1        00000        00000 
-     2        00000        00001 
-     3        00001        00001 
-     4        00001        00000 
-end coordinates 
- 
-elements 
-     1      1      2      3      4  1 
-end elements
-
diff --git a/myMesh.flavia.res b/myMesh.flavia.res
deleted file mode 100644
index d319acbe3f..0000000000
--- a/myMesh.flavia.res
+++ /dev/null
@@ -1,17 +0,0 @@
-GiD Post Results File 1.0 
-GaussPoints "Gauss Points" Elemtype Quadrilateral
-Number of Gauss Points: 1 
-Nodes not included 
-Natural Coordinates: given 
-       00000        00000 
-End GaussPoints  
-
-Result "fValues" "FunResults" 0 Scalar OnNodes 
-ComponentNames  "x"
-Values  
-1        00000 
-2        00000 
-3        00000 
-4        00000 
-End Values
-
diff --git a/myMesh.vtu b/myMesh.vtu
deleted file mode 100644
index b9f3068ad7..0000000000
--- a/myMesh.vtu
+++ /dev/null
@@ -1,28 +0,0 @@
-<?xml version="1.0" encoding="utf-8"?>
-<VTKFile byte_order="LittleEndian" type="UnstructuredGrid" version="0.1">
-   <UnstructuredGrid>
-      <Piece NumberOfCells="1" NumberOfPoints="4">
-         <Points>
-            <DataArray Name="Points" NumberOfComponents="3" format="ascii" type="Float32">
-0.0000 0.0000 0.0000
-0.0000 1.0000 0.0000
-1.0000 1.0000 0.0000
-1.0000 0.0000 0.0000</DataArray>
-         </Points>
-         <Cells>
-            <DataArray Name="connectivity" format="ascii" type="Int32">
- 0 1 2 3</DataArray>
-            <DataArray Name="offsets" format="ascii" type="Int32">4 </DataArray>
-            <DataArray Name="types" format="ascii" type="UInt8">9 </DataArray>
-         </Cells>
-         <PointData>
-            <DataArray Name="fValues" NumberOfComponents="1" format="ascii" type="Float64">
-       00000 
-       00000 
-       00000 
-       00000 </DataArray>
-         </PointData>
-         <CellData/>
-      </Piece>
-   </UnstructuredGrid>
-</VTKFile>
\ No newline at end of file
diff --git a/ns_pau_tarres/LHSintegrator_NonLinearNS.m b/ns_pau_tarres/LHSintegrator_NonLinearNS.m
new file mode 100644
index 0000000000..5af0a44dd7
--- /dev/null
+++ b/ns_pau_tarres/LHSintegrator_NonLinearNS.m
@@ -0,0 +1,70 @@
+classdef LHSintegrator_NonLinearNS < LHSIntegrator
+
+    methods (Access = public)
+
+        function obj = LHSintegrator_NonLinearNS(cParams)
+            obj@LHSIntegrator(cParams)
+        end
+
+        function LHS = compute(obj, velocityField)
+            lhs = obj.computeElementalLHS(velocityField);
+            LHS = obj.assembleMatrix(lhs);
+        end
+
+    end
+
+    methods (Access = private)
+
+        function lhs = computeElementalLHS(obj, velocityField)
+            xV          = obj.quadrature.posgp;             
+            dNdxTest    = obj.test.evaluateCartesianDerivatives(xV);
+            dNdxTrial   = obj.trial.evaluateCartesianDerivatives(xV);
+            dVolu       = obj.mesh.computeDvolume(obj.quadrature);
+
+            NTest  = obj.test.computeShapeFunctions(xV);
+            NTrial = obj.trial.computeShapeFunctions(xV);
+
+            nGaus       = obj.quadrature.ngaus;
+            nElem       = size(dVolu, 2);
+            nNodeTest   = size(dNdxTest, 2);
+            nNodeTrial  = size(dNdxTrial, 2);
+            nDim        = size(dNdxTrial,1);
+            nDofTest    = nNodeTest * obj.test.ndimf;
+            nDofTrial   = nNodeTrial * obj.trial.ndimf;
+
+            C = zeros(nDofTest, nDofTrial, nElem);
+            uValues = velocityField.evaluate(xV);
+
+            
+            for igauss = 1:nGaus
+                u_gp = squeeze(uValues(:, igauss, :));  % [nDim x nElem]
+                dV   = dVolu(igauss, :);                % [1 x nElem]
+            
+                for idof = 1:nNodeTest
+                    phi_i = NTest(idof, igauss);        % scalar
+            
+                    for jdof = 1:nNodeTrial
+                        grad_phi_j = squeeze(dNdxTrial(:, jdof, igauss, :)); % [nDim x nElem]
+            
+                        for alpha = 1:nDim
+                            idof2 = nDim * (idof - 1) + alpha;
+            
+                            for beta = 1:nDim
+                                jdof2 = nDim * (jdof - 1) + beta;
+                                conv_term = u_gp(beta, :) .* grad_phi_j(beta, :);  % [1 x nElem]
+            
+                                % update matrix entry
+                                C(idof2, jdof2, :) = C(idof2, jdof2, :) + ...
+                                    reshape(phi_i * conv_term .* dV, [1 1 nElem]);
+                            end
+                        end
+                    end
+                end
+            end
+
+
+            lhs = C;
+        end
+
+    end
+end
diff --git a/ns_pau_tarres/linear_elasticity/linear_elasticity_fbs.m b/ns_pau_tarres/linear_elasticity/linear_elasticity_fbs.m
new file mode 100644
index 0000000000..085bdf8930
--- /dev/null
+++ b/ns_pau_tarres/linear_elasticity/linear_elasticity_fbs.m
@@ -0,0 +1,125 @@
+clear
+clc
+
+% =========================================================================
+% =========================================================================
+%                      COMPRESSIBLE LINEAR ELASTICITY
+% =========================================================================
+% =========================================================================
+
+% =========================================================================
+% 1) CREATE MESH
+% =========================================================================
+mesh = UnitTriangleMesh(100,100);
+
+% =========================================================================
+% 2) CREATE FINITE ELEMENT FUNCTIONS (velocity u, pressure p)
+% =========================================================================
+u = LagrangianFunction.create(mesh, 2, 'P1');
+n_dofs = u.nDofs;
+
+% =========================================================================
+% 3) SET UP BOUNDARY CONDITIONS (Dirichlet)
+% =========================================================================
+isLeft   = @(coor) (abs(coor(:,1) - min(coor(:,1))) < 1e-12);
+isRight  = @(coor) (abs(coor(:,1) - max(coor(:,1))) < 1e-12);
+isBottom = @(coor) (abs(coor(:,2) - min(coor(:,2))) < 1e-12);
+isTop    = @(coor) (abs(coor(:,2) - max(coor(:,2))) < 1e-12);
+
+dir.domain    = @(coor) isLeft(coor);
+dir.direction = [1,2];
+dir.value     = [0,0]; 
+dirichlet = DirichletCondition(mesh, dir);
+
+neu.domain = @(coor) isRight(coor);
+neu.direction = [1,2];
+neu.value     = [0,-1]; 
+neumann = DirichletCondition(mesh, neu);
+
+c.mesh = mesh;
+c.dirichletFun = dirichlet;
+c.pointloadFun = neumann;
+c.periodicFun = [];
+bc = BoundaryConditions(c);
+
+E         = ConstantFunction.create(1,mesh);
+nu        = ConstantFunction.create(1/3,mesh);
+s.ptype   = 'ELASTIC';
+s.pdim    = '2D';
+s.nelem   = mesh.nelem;
+s.mesh    = mesh;
+s.young   = E;
+s.poisson = nu;
+s.type = 'ISOTROPIC';
+s.ndim = mesh.ndim;
+material = Material.create(s);
+
+% =========================================================================
+% 5) BUILD MATRICES
+% =========================================================================
+% 1) Diffusion (viscous) part
+s1.type  = 'ElasticStiffnessMatrix';
+s1.mesh  = mesh;
+s1.test     = u;
+s1.trial    = u;
+s1.material = material;
+s1.quadratureOrder = 2;
+LHS1 = LHSIntegrator.create(s1);
+K = LHS1.compute();
+
+% 2) Forces vector
+s2.type     = 'Elastic';
+s2.scale    = 'MACRO';
+s2.dim.ndimf = mesh.ndim;
+s2.dim.nnodes = mesh.nnodes;
+s2.dim.ndofs = s2.dim.nnodes * s2.dim.ndimf;
+s2.dim.nnodeElem = mesh.nnodeElem;
+s2.dim.ndofsElem = s2.dim.ndimf * s2.dim.nnodeElem;
+s2.BC       = bc;
+s2.mesh     = mesh;
+s2.material = material;
+s2.globalConnec = mesh.connec;
+RHSint = RHSIntegrator.create(s2);
+F = RHSint.compute();
+
+% =========================================================================
+% 6) SOLVE SYSTEM (Monolithic)
+% =========================================================================
+
+all_dofs  = 1:u.nDofs;
+free = setdiff(all_dofs , bc.dirichlet_dofs);
+
+U_new = zeros(u.nDofs,1);
+
+maxIter = 2000000;
+rtol = 3e-6;
+tau = 0.3;
+
+for k = 1:maxIter
+    U = U_new;
+
+    % -- gradient step
+    grad = K*U - F;
+    U_new = U - tau*grad;
+    
+    % -- proximal operator = impose Dirichlet values
+    U_new(bc.dirichlet_dofs) = bc.dirichlet_vals;
+        
+    % -- convergence test
+    res = norm(U_new-U) / max(1,norm(U));
+    if res < rtol
+        fprintf('Converged in %d iterations\n',k);
+        break
+    end
+
+    if mod(k,100) == 0
+        fprintf('Residual at iteration %i: %d\n',k, res);
+    end
+end
+
+u.setFValues(reshape(U_new,2,[])');
+
+% =========================================================================
+% 7) PLOT RESULTS
+% =========================================================================
+u.plot();
diff --git a/ns_pau_tarres/linear_elasticity/linear_elasticity_monolithic.m b/ns_pau_tarres/linear_elasticity/linear_elasticity_monolithic.m
new file mode 100644
index 0000000000..15166ed1b5
--- /dev/null
+++ b/ns_pau_tarres/linear_elasticity/linear_elasticity_monolithic.m
@@ -0,0 +1,107 @@
+clear
+clc
+
+% =========================================================================
+% =========================================================================
+%                      COMPRESSIBLE LINEAR ELASTICITY
+% =========================================================================
+% =========================================================================
+
+% =========================================================================
+% 1) CREATE MESH
+% =========================================================================
+mesh = UnitTriangleMesh(100,100);
+
+% =========================================================================
+% 2) CREATE FINITE ELEMENT FUNCTIONS (velocity u, pressure p)
+% =========================================================================
+u = LagrangianFunction.create(mesh, 2, 'P1');
+n_dofs = u.nDofs;
+
+% =========================================================================
+% 3) SET UP BOUNDARY CONDITIONS (Dirichlet)
+% =========================================================================
+isLeft   = @(coor) (abs(coor(:,1) - min(coor(:,1))) < 1e-12);
+isRight  = @(coor) (abs(coor(:,1) - max(coor(:,1))) < 1e-12);
+isBottom = @(coor) (abs(coor(:,2) - min(coor(:,2))) < 1e-12);
+isTop    = @(coor) (abs(coor(:,2) - max(coor(:,2))) < 1e-12);
+
+dir.domain    = @(coor) isLeft(coor);
+dir.direction = [1,2];
+dir.value     = [0,0]; 
+dirichlet = DirichletCondition(mesh, dir);
+
+neu.domain = @(coor) isRight(coor);
+neu.direction = [1,2];
+neu.value     = [0,-1]; 
+neumann = DirichletCondition(mesh, neu);
+
+c.mesh = mesh;
+c.dirichletFun = dirichlet;
+c.pointloadFun = neumann;
+c.periodicFun = [];
+bc = BoundaryConditions(c);
+
+E         = ConstantFunction.create(1,mesh);
+nu        = ConstantFunction.create(1/3,mesh);
+s.ptype   = 'ELASTIC';
+s.pdim    = '2D';
+s.nelem   = mesh.nelem;
+s.mesh    = mesh;
+s.young   = E;
+s.poisson = nu;
+s.type = 'ISOTROPIC';
+s.ndim = mesh.ndim;
+material = Material.create(s);
+
+% =========================================================================
+% 5) BUILD MATRICES
+% =========================================================================
+% 1) Diffusion (viscous) part
+s1.type  = 'ElasticStiffnessMatrix';
+s1.mesh  = mesh;
+s1.test     = u;
+s1.trial    = u;
+s1.material = material;
+s1.quadratureOrder = 2;
+LHS1 = LHSIntegrator.create(s1);
+K = LHS1.compute();
+
+% 2) Forces vector
+s2.type     = 'Elastic';
+s2.scale    = 'MACRO';
+s2.dim.ndimf = mesh.ndim;
+s2.dim.nnodes = mesh.nnodes;
+s2.dim.ndofs = s2.dim.nnodes * s2.dim.ndimf;
+s2.dim.nnodeElem = mesh.nnodeElem;
+s2.dim.ndofsElem = s2.dim.ndimf * s2.dim.nnodeElem;
+s2.BC       = bc;
+s2.mesh     = mesh;
+s2.material = material;
+s2.globalConnec = mesh.connec;
+RHSint = RHSIntegrator.create(s2);
+F = RHSint.compute();
+
+% 3) C
+n_dir_dofs = length(bc.dirichlet_dofs);
+C = sparse(bc.dirichlet_dofs, 1:n_dir_dofs, 1, n_dofs, n_dir_dofs);
+
+% 4) 0
+O = zeros(length(bc.dirichlet_dofs));
+
+% =========================================================================
+% 6) SOLVE SYSTEM (Monolithic)
+% =========================================================================
+
+LHS = [K C; C' O];
+RHS = [F; bc.dirichlet_vals];
+
+vars = LHS \ RHS;
+U = vars(1:n_dofs);
+lambda = vars(1+n_dofs:end);
+u.setFValues(reshape(U,2,[])');
+
+% =========================================================================
+% 7) PLOT RESULTS
+% =========================================================================
+u.plot();
diff --git a/ns_pau_tarres/linear_elasticity/linear_elasticity_segmentation.m b/ns_pau_tarres/linear_elasticity/linear_elasticity_segmentation.m
new file mode 100644
index 0000000000..3a4e55e2f0
--- /dev/null
+++ b/ns_pau_tarres/linear_elasticity/linear_elasticity_segmentation.m
@@ -0,0 +1,104 @@
+clear
+clc
+
+% =========================================================================
+% =========================================================================
+%                      COMPRESSIBLE LINEAR ELASTICITY
+% =========================================================================
+% =========================================================================
+
+% =========================================================================
+% 1) CREATE MESH
+% =========================================================================
+mesh = UnitTriangleMesh(100,100);
+
+% =========================================================================
+% 2) CREATE FINITE ELEMENT FUNCTIONS (velocity u, pressure p)
+% =========================================================================
+u = LagrangianFunction.create(mesh, 2, 'P1');
+n_dofs = u.nDofs;
+
+% =========================================================================
+% 3) SET UP BOUNDARY CONDITIONS (Dirichlet)
+% =========================================================================
+isLeft   = @(coor) (abs(coor(:,1) - min(coor(:,1))) < 1e-12);
+isRight  = @(coor) (abs(coor(:,1) - max(coor(:,1))) < 1e-12);
+isBottom = @(coor) (abs(coor(:,2) - min(coor(:,2))) < 1e-12);
+isTop    = @(coor) (abs(coor(:,2) - max(coor(:,2))) < 1e-12);
+
+dir.domain    = @(coor) isLeft(coor);
+dir.direction = [1,2];
+dir.value     = [0,0]; 
+dirichlet = DirichletCondition(mesh, dir);
+
+neu.domain = @(coor) isRight(coor);
+neu.direction = [1,2];
+neu.value     = [0,-1]; 
+neumann = DirichletCondition(mesh, neu);
+
+c.mesh = mesh;
+c.dirichletFun = dirichlet;
+c.pointloadFun = neumann;
+c.periodicFun = [];
+bc = BoundaryConditions(c);
+
+E         = ConstantFunction.create(1,mesh);
+nu        = ConstantFunction.create(1/3,mesh);
+s.ptype   = 'ELASTIC';
+s.pdim    = '2D';
+s.nelem   = mesh.nelem;
+s.mesh    = mesh;
+s.young   = E;
+s.poisson = nu;
+s.type = 'ISOTROPIC';
+s.ndim = mesh.ndim;
+material = Material.create(s);
+
+% =========================================================================
+% 5) BUILD MATRICES
+% =========================================================================
+% 1) Diffusion (viscous) part
+s1.type  = 'ElasticStiffnessMatrix';
+s1.mesh  = mesh;
+s1.test     = u;
+s1.trial    = u;
+s1.material = material;
+s1.quadratureOrder = 2;
+LHS1 = LHSIntegrator.create(s1);
+K = LHS1.compute();
+
+% 2) Forces vector
+s2.type     = 'Elastic';
+s2.scale    = 'MACRO';
+s2.dim.ndimf = mesh.ndim;
+s2.dim.nnodes = mesh.nnodes;
+s2.dim.ndofs = s2.dim.nnodes * s2.dim.ndimf;
+s2.dim.nnodeElem = mesh.nnodeElem;
+s2.dim.ndofsElem = s2.dim.ndimf * s2.dim.nnodeElem;
+s2.BC       = bc;
+s2.mesh     = mesh;
+s2.material = material;
+s2.globalConnec = mesh.connec;
+RHSint = RHSIntegrator.create(s2);
+F = RHSint.compute();
+
+
+% =========================================================================
+% 6) SOLVE SYSTEM (Monolithic)
+% =========================================================================
+
+all_dofs = 1:u.nDofs;
+free_dofs = setdiff(all_dofs, bc.dirichlet_dofs);
+
+K_r = K(free_dofs, free_dofs);
+F_r = F(free_dofs);
+
+U = zeros(u.nDofs,1);
+U(free_dofs) = K_r \ F_r;
+U(bc.dirichlet_dofs) = bc.dirichlet_vals(bc.dirichlet_dofs);
+u.setFValues(reshape(U,2,[])');
+
+% =========================================================================
+% 7) PLOT RESULTS
+% =========================================================================
+u.plot();
diff --git a/ns_pau_tarres/linear_elasticity/linear_elasticity_segmentation_fbs.m b/ns_pau_tarres/linear_elasticity/linear_elasticity_segmentation_fbs.m
new file mode 100644
index 0000000000..6386848482
--- /dev/null
+++ b/ns_pau_tarres/linear_elasticity/linear_elasticity_segmentation_fbs.m
@@ -0,0 +1,132 @@
+clear
+clc
+
+% =========================================================================
+% =========================================================================
+%                      COMPRESSIBLE LINEAR ELASTICITY
+% =========================================================================
+% =========================================================================
+
+% =========================================================================
+% 1) CREATE MESH
+% =========================================================================
+mesh = UnitTriangleMesh(100,100);
+
+% =========================================================================
+% 2) CREATE FINITE ELEMENT FUNCTIONS (velocity u, pressure p)
+% =========================================================================
+u = LagrangianFunction.create(mesh, 2, 'P1');
+n_dofs = u.nDofs;
+
+% =========================================================================
+% 3) SET UP BOUNDARY CONDITIONS (Dirichlet)
+% =========================================================================
+isLeft   = @(coor) (abs(coor(:,1) - min(coor(:,1))) < 1e-12);
+isRight  = @(coor) (abs(coor(:,1) - max(coor(:,1))) < 1e-12);
+isBottom = @(coor) (abs(coor(:,2) - min(coor(:,2))) < 1e-12);
+isTop    = @(coor) (abs(coor(:,2) - max(coor(:,2))) < 1e-12);
+
+dir.domain    = @(coor) isLeft(coor);
+dir.direction = [1,2];
+dir.value     = [0,0]; 
+dirichlet = DirichletCondition(mesh, dir);
+
+neu.domain = @(coor) isRight(coor);
+neu.direction = [1,2];
+neu.value     = [0,-1]; 
+neumann = DirichletCondition(mesh, neu);
+
+c.mesh = mesh;
+c.dirichletFun = dirichlet;
+c.pointloadFun = neumann;
+c.periodicFun = [];
+bc = BoundaryConditions(c);
+
+E         = ConstantFunction.create(1,mesh);
+nu        = ConstantFunction.create(1/3,mesh);
+s.ptype   = 'ELASTIC';
+s.pdim    = '2D';
+s.nelem   = mesh.nelem;
+s.mesh    = mesh;
+s.young   = E;
+s.poisson = nu;
+s.type = 'ISOTROPIC';
+s.ndim = mesh.ndim;
+material = Material.create(s);
+
+% =========================================================================
+% 5) BUILD MATRICES
+% =========================================================================
+% 1) Diffusion (viscous) part
+s1.type  = 'ElasticStiffnessMatrix';
+s1.mesh  = mesh;
+s1.test     = u;
+s1.trial    = u;
+s1.material = material;
+s1.quadratureOrder = 2;
+LHS1 = LHSIntegrator.create(s1);
+K = LHS1.compute();
+
+% 2) Forces vector
+s2.type     = 'Elastic';
+s2.scale    = 'MACRO';
+s2.dim.ndimf = mesh.ndim;
+s2.dim.nnodes = mesh.nnodes;
+s2.dim.ndofs = s2.dim.nnodes * s2.dim.ndimf;
+s2.dim.nnodeElem = mesh.nnodeElem;
+s2.dim.ndofsElem = s2.dim.ndimf * s2.dim.nnodeElem;
+s2.BC       = bc;
+s2.mesh     = mesh;
+s2.material = material;
+s2.globalConnec = mesh.connec;
+RHSint = RHSIntegrator.create(s2);
+F = RHSint.compute();
+
+
+% =========================================================================
+% 6) SOLVE SYSTEM (Monolithic)
+% =========================================================================
+
+all_dofs  = 1:u.nDofs;
+free = setdiff(all_dofs , bc.dirichlet_dofs);
+
+U = zeros(u.nDofs,1);
+
+maxIter = 2000000;
+rtol = 3e-6;
+
+K_r  = K(free,free);
+F_r  = F(free);
+
+tau = 0.32;
+
+for k = 1:maxIter
+    U_new = U;
+
+    % -- gradient step on the FREE dofs only
+    grad = K_r*U(free) - F_r;
+    U_new(free) = U(free) - tau*grad;
+    
+    % -- proximal operator = impose Dirichlet values
+    U_new(bc.dirichlet_dofs) = bc.dirichlet_vals;
+        
+    % -- convergence test
+    res = norm(U_new-U) / max(1,norm(U));
+    if res < rtol
+        fprintf('Converged in %d iterations\n',k);
+        break
+    end
+
+    if mod(k,100) == 0
+        fprintf('Residual at iteration %i: %d\n',k, res);
+    end
+
+    U = U_new;
+end
+
+u.setFValues(reshape(U_new,2,[])');
+
+% =========================================================================
+% 7) PLOT RESULTS
+% =========================================================================
+u.plot();
diff --git a/ns_pau_tarres/navier_stokes/ns_fractional_step_steady.m b/ns_pau_tarres/navier_stokes/ns_fractional_step_steady.m
new file mode 100644
index 0000000000..92e2faf64d
--- /dev/null
+++ b/ns_pau_tarres/navier_stokes/ns_fractional_step_steady.m
@@ -0,0 +1,126 @@
+% =========================================================================
+% INCOMPRESSIBLE NAVIER–STOKES WITH PICARD + PROJECTION
+% =========================================================================
+clear; clc;
+
+% CREATE MESH
+mesh = UnitTriangleMesh(100,100);
+
+% DEFINE FE SPACES
+u     = LagrangianFunction.create(mesh, 2, 'P2');
+p     = LagrangianFunction.create(mesh, 1, 'P1');
+u_nd  = u.nDofs;
+p_nd  = p.nDofs;
+
+% BOUNDARY CONDITIONS for velocity (Dirichlet)
+isLeft   = @(coor) (abs(coor(:,1) - min(coor(:,1)))   < 1e-12);
+isRight  = @(coor) (abs(coor(:,1) - max(coor(:,1)))   < 1e-12);
+isBottom = @(coor) (abs(coor(:,2) - min(coor(:,2)))   < 1e-12);
+isTop    = @(coor) (abs(coor(:,2) - max(coor(:,2)))   < 1e-12);
+
+dir_vel{1}.domain    = @(coor) isTop(coor);
+dir_vel{1}.direction = [1,2];
+dir_vel{1}.value     = [1,0];
+
+dir_vel{2}.domain    = @(coor) (isBottom(coor) | isRight(coor) | isLeft(coor)) & not(isTop(coor));
+dir_vel{2}.direction = [1,2];
+dir_vel{2}.value     = [0,0]; 
+
+dirichlet = [];
+dir_dofs = [];
+for i = 1:length(dir_vel)
+    dirDofs = u.getDofsFromCondition(dir_vel{i}.domain);
+    nodes = 1 + (dirDofs(2:2:end) - 2) / u.ndimf;
+    iNod = repelem(nodes, 2)';
+    dofType = repmat((1:2)', length(nodes), 1);
+    valmat = repmat(dir_vel{i}.value', length(nodes), 1);
+    dirichlet = [dirichlet; [iNod', dofType, valmat]];
+    dir_dofs = [dir_dofs; dirDofs(:)];
+end
+
+% FORCES
+sf.mesh    = mesh;
+sf.ndimf   = 2;
+sf.fHandle = @(coor) [0*coor,0*coor];
+forces = AnalyticalFunction(sf);
+
+% BUILD MATRICES
+group.type  = 'MassMatrix';
+group.mesh  = mesh;
+group.test = u;
+group.trial = u;
+M = LHSIntegrator.create(group).compute();
+
+group.type = 'StiffnessMatrix';
+group.test = u;
+group.trial = u;
+K_u = LHSIntegrator.create(group).compute();
+
+group.type = 'StiffnessMatrix';
+group.test = p;
+group.trial = p;
+K_p = LHSIntegrator.create(group).compute();
+
+group.type = 'NonLinearNS';
+group.trial = u;
+group.test = u;
+ConvForm = LHSIntegrator.create(group);
+
+group.type = 'WeakDivergence';
+group.mesh = mesh;
+group.test = u;
+group.trial = p;
+D_weak = LHSIntegrator.create(group).compute();
+D = D_weak'; % div
+G = -D'; % gradient
+
+n_dir = length(dir_dofs);
+C = sparse(dir_dofs, 1:n_dir, 1, u.nDofs, n_dir);
+
+% TIME-STEPPING SETUP
+time_steps = 100;
+dt = 1e-4;
+nu = 1;
+maxPicardIts  = 300;
+utol = 1e-10;
+alpha = 0.7;
+
+u_k = reshape(u.fValues', [],1);
+K_p(1,:)=0; K_p(:,1)=0; K_p(1,1)=1;
+
+for pic = 1:maxPicardIts
+    u.setFValues(reshape(u_k,2,[])');
+    N = ConvForm.compute(u);
+
+    A = (1/dt)*M - N + nu*K_u;
+    LHS = [A, C; C', sparse(n_dir,n_dir)];
+    RHS = [(1/dt)*M*u_k; dirichlet(:,3)];
+    sol = LHS \ RHS;
+    u_ast = sol(1:u_nd);
+
+    rhs_p = D*u_ast/dt;
+    rhs_p(1)=0;
+    p_k1 = K_p \ rhs_p;
+
+    x = [M C; C' sparse(n_dir,n_dir)] \ [(M*u_ast + dt * (G * p_k1)); dirichlet(:,3)];
+    u_k1 = x(1:u.nDofs);
+    u_k1 = u_k + alpha*(u_k1 - u_k);
+
+    velRes = norm(u_k1-u_k)/(norm(u_k1)+eps);
+    divRes = norm(D*u_k1);
+    fprintf('it=%d: uΔ=%.2e, div=%.2e\n',pic,velRes,divRes);
+    if velRes<utol
+        break;
+    end
+
+    u_k = u_k1;
+end
+
+u_k = u_k1;
+p_k = p_k1;
+u.setFValues(reshape(u_k,2,[])');
+p.setFValues(reshape(p_k,1,[])');
+
+% PLOT RESULTS
+u.plot();
+p.plot();
diff --git a/ns_pau_tarres/navier_stokes/ns_fractional_step_unsteady.m b/ns_pau_tarres/navier_stokes/ns_fractional_step_unsteady.m
new file mode 100644
index 0000000000..89b2511557
--- /dev/null
+++ b/ns_pau_tarres/navier_stokes/ns_fractional_step_unsteady.m
@@ -0,0 +1,137 @@
+% =========================================================================
+% INCOMPRESSIBLE NAVIER–STOKES WITH PICARD + PROJECTION
+% =========================================================================
+clear; clc;
+
+% CREATE MESH
+mesh = UnitTriangleMesh(100,100);
+
+% DEFINE FUNCTIONS
+u     = LagrangianFunction.create(mesh, 2, 'P2');
+p     = LagrangianFunction.create(mesh, 1, 'P1');
+u_nd  = u.nDofs;
+p_nd  = p.nDofs;
+
+% BOUNDARY CONDITIONS for velocity (Dirichlet)
+isLeft   = @(coor) (abs(coor(:,1) - min(coor(:,1)))   < 1e-12);
+isRight  = @(coor) (abs(coor(:,1) - max(coor(:,1)))   < 1e-12);
+isBottom = @(coor) (abs(coor(:,2) - min(coor(:,2)))   < 1e-12);
+isTop    = @(coor) (abs(coor(:,2) - max(coor(:,2)))   < 1e-12);
+
+dir_vel{1}.domain    = @(coor) isTop(coor);
+dir_vel{1}.direction = [1,2];
+dir_vel{1}.value     = [1,0];
+
+dir_vel{2}.domain    = @(coor) (isBottom(coor) | isRight(coor) | isLeft(coor)) & not(isTop(coor));
+dir_vel{2}.direction = [1,2];
+dir_vel{2}.value     = [0,0]; 
+
+dirichlet = [];
+dir_dofs = [];
+for i = 1:length(dir_vel)
+    dirDofs = u.getDofsFromCondition(dir_vel{i}.domain);
+    nodes = 1 + (dirDofs(2:2:end) - 2) / u.ndimf;
+    iNod = repelem(nodes, 2)';
+    dofType = repmat((1:2)', length(nodes), 1);
+    valmat = repmat(dir_vel{i}.value', length(nodes), 1);
+    dirichlet = [dirichlet; [iNod', dofType, valmat]];
+    dir_dofs = [dir_dofs; dirDofs(:)];
+end
+
+% FORCES
+sf.mesh    = mesh;
+sf.ndimf   = 2;
+sf.fHandle = @(coor) [0*coor,0*coor];
+forces = AnalyticalFunction(sf);
+
+% BUILD CONSTANT MATRICES
+group.type  = 'MassMatrix';
+group.mesh  = mesh;
+group.test = u;
+group.trial = u;
+M = LHSIntegrator.create(group).compute();
+
+group.type = 'StiffnessMatrix';
+group.test = u;
+group.trial = u;
+K_u = LHSIntegrator.create(group).compute();
+
+group.type = 'StiffnessMatrix';
+group.test = p;
+group.trial = p;
+K_p = LHSIntegrator.create(group).compute();
+
+group.type = 'NonLinearNS';
+group.trial = u;
+group.test = u;
+ConvForm = LHSIntegrator.create(group);
+
+group.type = 'WeakDivergence';
+group.mesh = mesh;
+group.test = u;
+group.trial = p;
+D_weak = LHSIntegrator.create(group).compute();
+D = D_weak'; % div
+G = -D'; % gradient
+
+n_dir = length(dir_dofs);
+C = sparse(dir_dofs, 1:n_dir, 1, u.nDofs, n_dir);
+
+% TIME-STEPPING SETUP
+time_steps = 100;
+dt = 1e-1;
+nu = 1;
+maxPicardIts = 20;
+utol = 1e-7;
+ptol = 1;
+alpha = 0.7;
+
+% initial
+u_k = reshape(u.fValues', [],1);
+p_k = reshape(p.fValues', [],1);
+K_p(1,:)=0; K_p(:,1)=0; K_p(1,1)=1;
+
+% TIME LOOP
+for t = 1:time_steps
+    % Picard initialize
+    u_old = u_k;
+    p_old = p_k;
+
+    for pic = 1:maxPicardIts
+        u.setFValues(reshape(u_old,2,[])');
+        N = ConvForm.compute(u);
+
+        A = (1/dt)*M - N + nu*K_u;
+        LHS = [A, C; C', sparse(n_dir,n_dir)];
+        RHS = [(1/dt)*M*u_k; dirichlet(:,3)];
+        sol = LHS \ RHS;
+        u_ast = sol(1:u_nd);
+
+        rhs_p = D*u_ast/dt;
+        rhs_p(1)=0;
+        p_new = K_p \ rhs_p;
+
+        x = [M C; C' sparse(n_dir,n_dir)] \ [(M*u_ast + dt * (G * p_new)); dirichlet(:,3)];
+        u_corr = x(1:u.nDofs);
+        u_new = u_old + alpha*(u_corr - u_old);
+
+        velRes = norm(u_new-u_old)/(norm(u_new)+eps);
+        divRes = norm(D*u_new);
+        fprintf('t=%d pic=%d: uΔ=%.2e, div=%.2e\n',t,pic,velRes,divRes);
+        if velRes<utol && divRes<ptol
+            break;
+        end
+
+        u_old = u_new;
+        p_old = p_new;
+    end
+
+    u_k = u_new;
+    p_k = p_new;
+    u.setFValues(reshape(u_k,2,[])');
+    p.setFValues(reshape(p_k,1,[])');
+    fprintf('Completed time step %d in %d Picard iterations.\n',t,pic);
+end
+
+u.plot();
+p.plot();
diff --git a/ns_pau_tarres/navier_stokes/ns_picard_monolithic.m b/ns_pau_tarres/navier_stokes/ns_picard_monolithic.m
new file mode 100644
index 0000000000..422d594edd
--- /dev/null
+++ b/ns_pau_tarres/navier_stokes/ns_picard_monolithic.m
@@ -0,0 +1,182 @@
+
+clear
+clc
+
+% =========================================================================
+% 1) CREATE MESH
+% =========================================================================
+mesh = UnitTriangleMesh(100,100);
+
+% =========================================================================
+% 2) CREATE FINITE ELEMENT FUNCTIONS (velocity u, pressure p)
+% =========================================================================
+u = LagrangianFunction.create(mesh, 2, 'P2');
+p = LagrangianFunction.create(mesh, 1, 'P1');
+n_dofs = u.nDofs + p.nDofs;
+
+% =========================================================================
+% 3) SET UP BOUNDARY CONDITIONS (Dirichlet)
+% =========================================================================
+isLeft   = @(coor) (abs(coor(:,1) - min(coor(:,1)))   < 1e-12);
+isRight  = @(coor) (abs(coor(:,1) - max(coor(:,1)))   < 1e-12);
+isBottom = @(coor) (abs(coor(:,2) - min(coor(:,2)))   < 1e-12);
+isTop    = @(coor) (abs(coor(:,2) - max(coor(:,2)))   < 1e-12);
+
+dir_vel{1}.domain    = @(coor) isTop(coor);
+dir_vel{1}.direction = [1,2];
+dir_vel{1}.value     = [1,0];
+
+dir_vel{2}.domain    = @(coor) (isBottom(coor) | isRight(coor) | isLeft(coor)) & not(isTop(coor));
+dir_vel{2}.direction = [1,2];
+dir_vel{2}.value     = [0,0]; 
+
+dirichlet = [];
+dir_dofs = [];
+for i = 1:length(dir_vel)
+    dirDofs = u.getDofsFromCondition(dir_vel{i}.domain);
+    nodes = 1 + (dirDofs(2:2:end) - 2) / u.ndimf;
+    iNod = repelem(nodes, 2)';
+    dofType = repmat((1:2)', length(nodes), 1);
+    valmat = repmat(dir_vel{i}.value', length(nodes), 1);
+    dirichlet = [dirichlet; [iNod', dofType, valmat]];
+    dir_dofs = [dir_dofs; dirDofs(:)];
+end
+
+% =========================================================================
+% 4) APPLIED FORCES
+% =========================================================================
+sAF.fHandle = @(coor) [0.*coor,0.*coor];
+sAF.ndimf   = 2;
+sAF.mesh    = mesh;
+forcesFormula = AnalyticalFunction(sAF);
+
+% =========================================================================
+% 5) BUILD MATRICES FOR THE LINEAR STOKES PROBLEM
+% =========================================================================
+% (a) Diffusion / stiffness matrix
+s1.type  = 'StiffnessMatrix';
+s1.mesh  = mesh;
+s1.test  = u;
+s1.trial = u;
+LHS1 = LHSIntegrator.create(s1);
+K = LHS1.compute();
+
+% (b) Divergence matrix
+s2.type = 'WeakDivergence';
+s2.mesh = mesh;
+s2.trial = p;
+s2.test  = u;
+LHS2 = LHSIntegrator.create(s2);
+D = LHS2.compute();
+
+% (c) Forces vector
+s3.type          = 'Stokes';
+s3.mesh          = mesh;
+s3.velocityFun   = u;
+s3.pressureFun   = p;
+s3.forcesFormula = forcesFormula;
+RHSint = RHSIntegrator.create(s3);
+F = RHSint.integrate();
+
+% (d) Nonlinear convective term
+s4.type = 'NonLinearNS';
+s4.mesh = mesh;
+s4.trial = u;
+s4.test = u;
+LHS4 = LHSIntegrator.create(s4);
+
+% C
+n_dir = length(dir_dofs);
+C = sparse(dir_dofs, 1:n_dir, 1, u.nDofs, n_dir);
+
+% 0
+O1 = zeros(p.nDofs);
+O2 = zeros(p.nDofs, n_dir);
+O3 = zeros(n_dir);
+O4 = zeros(p.nDofs, 1);
+
+RHS = [F; dirichlet(:,3)];
+pFix = 1;
+RHS(pFix + u.nDofs) = 0;
+
+% =========================================================================
+% 6) SOLVE SYSTEM
+% =========================================================================
+maxIter = 100;
+tol = 1e-8;
+x = zeros(length(RHS),1);
+x_prev = zeros(length(RHS),1);
+lambda = 1;
+
+nu = 1e-2;
+
+for iter = 1:maxIter
+
+    N = LHS4.compute(u);
+    
+    LHS = [nu*K+ N D C; D' O1 O2; C' O2' O3];
+    LHS(pFix + u.nDofs, :) = 0;
+    LHS(:, pFix + u.nDofs) = 0;
+    LHS(pFix + u.nDofs, pFix + u.nDofs) = 1;
+
+    x = LHS\RHS;
+    if ~isempty(dir_dofs)
+        x(dir_dofs) = dirichlet(:,3);
+    end
+    
+    vars.u = x(1:u.nDofs);
+    vars.p = x(u.nDofs+1:end);
+    
+    % Assign to FE functions
+    n_node = round(length(vars.u) / u.ndimf);
+    velfval = reshape(vars.u, u.ndimf, n_node)';
+    u.setFValues(velfval)
+    p.setFValues(vars.p)
+    
+    % Check convergence
+    norm_dx = norm(x - x_prev) / (norm(x) + eps);
+    fprintf('Picard Iteration %d: Relative Norm dx = %.3e\n', iter, norm_dx);
+    if norm_dx < tol
+        fprintf('Converged after %d Picard iterations.\n', iter);
+        break;
+    end
+    x_prev = x;
+end
+
+% =========================================================================
+% 7) EXTRACT AND PLOT THE RESULTS
+% =========================================================================
+uD  = dirichlet(:,3);
+if ~isempty(dir_dofs)
+    x(dir_dofs) = uD;
+end
+vars.u = x(1:u.nDofs);
+vars.p = x((1:p.nDofs) + u.nDofs);
+
+% Define final velocity/pressure
+n_node = round(length(vars.u)/u.ndimf);
+velfval = reshape(vars.u, u.ndimf, n_node)';
+u.setFValues(velfval)
+p.setFValues(vars.p)
+
+u.plot();
+p.plot();
+
+% Plot velocity profiles at mid-sections
+mid_x = 0.5;
+mid_idx = find(abs(mesh.coord(:,1) - mid_x) < 1e-3);
+figure;
+plot(mesh.coord(mid_idx,2), velfval(mid_idx,1), 'LineWidth', 2);
+xlabel('y-coordinate');
+ylabel('u-velocity');
+title('Velocity Profile at x = 0.5');
+grid on;
+
+mid_y = 0.5;
+mid_idy = find(abs(mesh.coord(:,2) - mid_y) < 1e-3);
+figure;
+plot(mesh.coord(mid_idy,1), velfval(mid_idy,2), 'LineWidth', 2);
+xlabel('x-coordinate');
+ylabel('v-velocity');
+title('Velocity Profile at y = 0.5');
+grid on;
diff --git a/ns_pau_tarres/stokes/stokes_fb.m b/ns_pau_tarres/stokes/stokes_fb.m
new file mode 100644
index 0000000000..c2f77cf2f7
--- /dev/null
+++ b/ns_pau_tarres/stokes/stokes_fb.m
@@ -0,0 +1,172 @@
+clear
+clc
+
+% =========================================================================
+% 1) CREATE MESH
+% =========================================================================
+mesh = UnitTriangleMesh(30,30);
+
+% =========================================================================
+% 2) CREATE FINITE ELEMENT FUNCTIONS (velocity u, pressure p)
+% =========================================================================
+u = LagrangianFunction.create(mesh, 2, 'P2');
+p = LagrangianFunction.create(mesh, 1, 'P1');
+n_dofs_u = u.nDofs;
+n_dofs_p = p.nDofs;
+n_dofs   = n_dofs_u + n_dofs_p;
+
+% =========================================================================
+% 3) SET UP BOUNDARY CONDITIONS (Dirichlet)
+% =========================================================================
+isLeft   = @(coor) abs(coor(:,1) - min(coor(:,1)))   < 1e-12;
+isRight  = @(coor) abs(coor(:,1) - max(coor(:,1)))   < 1e-12;
+isBottom = @(coor) abs(coor(:,2) - min(coor(:,2)))   < 1e-12;
+isTop    = @(coor) abs(coor(:,2) - max(coor(:,2)))   < 1e-12;
+
+dir_vel{1}.domain    = @(coor) isTop(coor);
+dir_vel{1}.direction = [1,2];
+dir_vel{1}.value     = [1,0];
+
+dir_vel{2}.domain    = @(coor) (isBottom(coor) | isRight(coor) | isLeft(coor)) & not(isTop(coor));
+dir_vel{2}.direction = [1,2];
+dir_vel{2}.value     = [0,0]; 
+
+dirichlet = [];
+dir_dofs = [];
+for i = 1:length(dir_vel)
+    dirDofs = u.getDofsFromCondition(dir_vel{i}.domain);
+    dofs   = 1 + (dirDofs(2:2:end) - 2) / u.ndimf;
+    iNod    = repelem(dofs, 2)';
+    dofType = repmat((1:2)', length(dofs), 1);
+    valmat  = repmat(dir_vel{i}.value', length(dofs), 1);
+    dirichlet  = [dirichlet; [iNod', dofType, valmat]];
+    dir_dofs   = [dir_dofs; dirDofs(:)];
+end
+
+% =========================================================================
+% 4) APPLIED FORCES
+% =========================================================================
+sAF.fHandle = @(coor) [0.*coor, 0.*coor];
+sAF.ndimf   = 2;
+sAF.mesh    = mesh;
+forcesFormula = AnalyticalFunction(sAF);
+
+% =========================================================================
+% 5) BUILD MATRICES FOR THE LINEAR STOKES PROBLEM
+% =========================================================================
+s1.type  = 'MassMatrix';
+s1.mesh  = mesh;
+s1.test  = u;
+s1.trial = u;
+LHS1 = LHSIntegrator.create(s1);
+M = LHS1.compute();
+
+s2.type  = 'StiffnessMatrix';
+s2.mesh  = mesh;
+s2.test  = u;
+s2.trial = u;
+LHS2 = LHSIntegrator.create(s2);
+K = LHS2.compute();
+
+s3.type  = 'WeakDivergence';
+s3.mesh  = mesh;
+s3.trial = p;
+s3.test  = u;
+LHS3 = LHSIntegrator.create(s3);
+B = LHS3.compute();
+
+s4.type = 'Stokes';
+s4.mesh = mesh;
+s4.velocityFun = u;
+s4.pressureFun = p;
+s4.forcesFormula = forcesFormula;
+RHSint = RHSIntegrator.create(s4);
+F = RHSint.integrate();
+F = F(1:n_dofs_u);
+
+O = zeros(n_dofs_p,n_dofs_p);
+o = zeros(n_dofs_p, 1);
+
+LHS = [M B; B' O];
+
+pFix = 1;
+LHS(pFix + u.nDofs, :) = 0;
+LHS(:, pFix + u.nDofs) = 0;
+LHS(pFix + u.nDofs, pFix + u.nDofs) = 1;
+RHS(pFix + u.nDofs) = 0;
+
+
+% =========================================================================
+% 6) FORWARD-BACKWARD ITERATION
+% =========================================================================
+maxIter = 200000;
+tol     = 1e-6;
+
+lambda = 0.17;
+
+u_k1 = zeros(n_dofs_u, 1);
+p_k1 = zeros(n_dofs_p, 1);
+
+for iter = 1:maxIter
+    u_k = u_k1;
+    p_k = p_k1;
+    gr = K*u_k - F;
+    u_ast = u_k - lambda*gr;
+    u_ast(dir_dofs) = dirichlet(:,3);
+    rhs = [M*u_ast; o];
+    vars = LHS \ rhs;
+    u_k1 = vars(1:n_dofs_u);
+    p_k1 = vars(1+n_dofs_u:end);
+
+    % ---------- convergence monitors ----------
+    step = norm(u_k1-u_k) / (norm(u_k) + eps);
+
+    % ---------- stop tests ----------
+    if step < 1e-6
+        fprintf('Converged in %d its: step %.1e\n', iter, step);
+        break
+    end
+
+    if mod(iter,10)==0
+        fprintf('it %4d | step %.3e \n', iter, step);
+    end
+end
+
+% =========================================================================
+% 7) EXTRACT AND PLOT THE RESULTS
+% =========================================================================
+% Store velocity values in a matrix for post-processing
+nu    = u.ndimf;
+nNode = round(length(u_k1)/nu);
+nodes = 1:nNode;
+velfval = zeros(nNode, nu);
+for idim = 1:nu
+    dofs = nu*(nodes-1) + idim;
+    velfval(:,idim) = u_k1(dofs);
+end
+u.setFValues(velfval);
+p.setFValues(p_k1);
+
+% Plot velocity and pressure solutions
+u.plot();
+p.plot();
+
+% Example velocity profile at x=0.5
+mid_x = 0.5;
+mid_idx = find(abs(mesh.coord(:,1) - mid_x) < 1e-3);
+figure;
+plot(mesh.coord(mid_idx,2), velfval(mid_idx,1), 'LineWidth', 2);
+xlabel('y-coordinate');
+ylabel('u-velocity');
+title('Velocity Profile at x = 0.5');
+grid on;
+
+% Example velocity profile at y=0.5
+mid_y = 0.5;
+mid_idy = find(abs(mesh.coord(:,2) - mid_y) < 1e-3);
+figure;
+plot(mesh.coord(mid_idy,1), velfval(mid_idy,2), 'LineWidth', 2);
+xlabel('x-coordinate');
+ylabel('v-velocity');
+title('Velocity Profile at y = 0.5');
+grid on;
diff --git a/ns_pau_tarres/stokes/stokes_fb_2.m b/ns_pau_tarres/stokes/stokes_fb_2.m
new file mode 100644
index 0000000000..421b5c2247
--- /dev/null
+++ b/ns_pau_tarres/stokes/stokes_fb_2.m
@@ -0,0 +1,184 @@
+clear
+clc
+
+% =========================================================================
+% 1) CREATE MESH
+% =========================================================================
+mesh = UnitTriangleMesh(40,40);
+
+% =========================================================================
+% 2) CREATE FINITE ELEMENT FUNCTIONS (velocity u, pressure p)
+% =========================================================================
+u = LagrangianFunction.create(mesh, 2, 'P2');
+p = LagrangianFunction.create(mesh, 1, 'P1');
+n_dofs = u.nDofs + p.nDofs;
+
+% =========================================================================
+% 3) SET UP BOUNDARY CONDITIONS (Dirichlet)
+% =========================================================================
+isLeft   = @(coor) (abs(coor(:,1) - min(coor(:,1)))   < 1e-12);
+isRight  = @(coor) (abs(coor(:,1) - max(coor(:,1)))   < 1e-12);
+isBottom = @(coor) (abs(coor(:,2) - min(coor(:,2)))   < 1e-12);
+isTop    = @(coor) (abs(coor(:,2) - max(coor(:,2)))   < 1e-12);
+
+dir_vel{1}.domain    = @(coor) isTop(coor);
+dir_vel{1}.direction = [1,2];
+dir_vel{1}.value     = [1,0];
+
+dir_vel{2}.domain    = @(coor) (isBottom(coor) | isRight(coor) | isLeft(coor)) & not(isTop(coor));
+dir_vel{2}.direction = [1,2];
+dir_vel{2}.value     = [0,0]; 
+
+dirichlet = [];
+dir_dofs = [];
+for i = 1:length(dir_vel)
+    dirDofs = u.getDofsFromCondition(dir_vel{i}.domain);
+    nodes = 1 + (dirDofs(2:2:end) - 2) / u.ndimf;
+    iNod = repelem(nodes, 2)';
+    dofType = repmat((1:2)', length(nodes), 1);
+    valmat = repmat(dir_vel{i}.value', length(nodes), 1);
+    dirichlet = [dirichlet; [iNod', dofType, valmat]];
+    dir_dofs = [dir_dofs; dirDofs(:)];
+end
+
+% =========================================================================
+% 4) APPLIED FORCES
+% =========================================================================
+sAF.fHandle = @(coor) [0.*coor,0.*coor];
+sAF.ndimf   = 2;
+sAF.mesh    = mesh;
+forcesFormula = AnalyticalFunction(sAF);
+
+% =========================================================================
+% 5) BUILD MATRICES FOR THE LINEAR STOKES PROBLEM
+% =========================================================================
+s1.type  = 'MassMatrix';
+s1.mesh  = mesh;
+s1.test  = u;
+s1.trial = u;
+LHS1 = LHSIntegrator.create(s1);
+M = LHS1.compute();
+
+% (a) Diffusion / stiffness matrix
+s1.type  = 'StiffnessMatrix';
+s1.mesh  = mesh;
+s1.test  = u;
+s1.trial = u;
+LHS1 = LHSIntegrator.create(s1);
+K = LHS1.compute();
+
+% (b) Divergence matrix
+s2.type = 'WeakDivergence';
+s2.mesh = mesh;
+s2.trial = p;
+s2.test  = u;
+LHS2 = LHSIntegrator.create(s2);
+B = LHS2.compute();
+
+% (c) Forces vector
+s3.type          = 'Stokes';
+s3.mesh          = mesh;
+s3.velocityFun   = u;
+s3.pressureFun   = p;
+s3.forcesFormula = forcesFormula;
+RHSint = RHSIntegrator.create(s3);
+F = RHSint.integrate();
+
+% C
+n_dir = length(dir_dofs);
+C = sparse(dir_dofs, 1:n_dir, 1, u.nDofs, n_dir);
+
+% 0
+O1 = zeros(p.nDofs);
+O2 = zeros(p.nDofs, n_dir);
+O3 = zeros(n_dir);
+O4 = zeros(p.nDofs, 1);
+o = zeros(p.nDofs, 1);
+
+
+% =========================================================================
+% 6) SOLVE SYSTEM
+% =========================================================================
+LHS = [M B C; B' O1 O2; C' O2' O3];
+RHS = [F; dirichlet(:,3)];
+
+pFix = 1;
+LHS(pFix + u.nDofs, :) = 0;
+LHS(:, pFix + u.nDofs) = 0;
+LHS(pFix + u.nDofs, pFix + u.nDofs) = 1;
+RHS(pFix + u.nDofs) = 0;
+
+maxIter = 200000;
+tol     = 1e-6;
+
+lambda = 0.15;
+
+u_k1 = zeros(u.nDofs, 1);
+p_k1 = zeros(p.nDofs, 1);
+
+for iter = 1:maxIter
+    u_k = u_k1;
+    p_k = p_k1;
+    u_ast = u_k - lambda*(K*u_k - F(1:u.nDofs));
+    RHS = [M*u_ast; o; dirichlet(:,3)];
+    vars = LHS \ RHS;
+    u_k1 = vars(1:u.nDofs);
+    p_k1 = vars(u.nDofs+(1:p.nDofs));
+
+    % ---------- convergence monitors ----------
+    step = norm(u_k1-u_k) / (norm(u_k) + eps);
+
+    % ---------- stop tests ----------
+    if step < 1e-6
+        fprintf('Converged in %d its: step %.1e\n', iter, step);
+        break
+    end
+
+    if mod(iter,1)==0
+        fprintf('it %4d | step %.3e \n', iter, step);
+    end
+end
+
+
+% =========================================================================
+% 7) EXTRACT AND PLOT THE RESULTS
+% =========================================================================
+% SEPARATE VARIABLES FVALUES
+var.u = u_k1;
+var.p = p_k1;
+
+% DEFINE VARIABLES
+nu = u.ndimf;
+nnode = round(length(var.u)/nu);
+nodes = 1:nnode;
+velfval = zeros(nnode,nu);
+for idim = 1:nu
+    dofs = nu*(nodes-1)+idim;
+    velfval(:,idim) = var.u(dofs, end);
+end
+u.setFValues(velfval)
+p.setFValues(var.p)
+
+% PLOT RESULTS
+u.plot();
+p.plot();
+
+% Example: velocity profile at x=0.5
+mid_x = 0.5;
+mid_idx = find(abs(mesh.coord(:,1) - mid_x) < 1e-3);
+figure;
+plot(mesh.coord(mid_idx,2), velfval(mid_idx,1), 'LineWidth', 2);
+xlabel('y-coordinate');
+ylabel('u-velocity');
+title('Velocity Profile at x = 0.5');
+grid on;
+
+% Example: velocity profile at y=0.5
+mid_y = 0.5;
+mid_idy = find(abs(mesh.coord(:,2) - mid_y) < 1e-3);
+figure;
+plot(mesh.coord(mid_idy,1), velfval(mid_idy,2), 'LineWidth', 2);
+xlabel('x-coordinate');
+ylabel('v-velocity');
+title('Velocity Profile at y = 0.5');
+grid on;
diff --git a/ns_pau_tarres/stokes/stokes_fb_lumped.m b/ns_pau_tarres/stokes/stokes_fb_lumped.m
new file mode 100644
index 0000000000..0e5ac8aba0
--- /dev/null
+++ b/ns_pau_tarres/stokes/stokes_fb_lumped.m
@@ -0,0 +1,167 @@
+%% 0) HOUSEKEEPING
+clear; clc;
+
+% =========================================================================
+% 1) CREATE MESH
+% =========================================================================
+mesh = UnitTriangleMesh(100,100);
+
+% =========================================================================
+% 2) CREATE FINITE-ELEMENT FUNCTIONS (velocity u, pressure p)
+% =========================================================================
+u = LagrangianFunction.create(mesh, 2, 'P2');
+p = LagrangianFunction.create(mesh, 1, 'P1');
+n_dofs_u = u.nDofs;
+n_dofs_p = p.nDofs;
+n_dofs   = n_dofs_u + n_dofs_p;
+
+% =========================================================================
+% 3) DIRICHLET BOUNDARY CONDITIONS
+% =========================================================================
+isLeft   = @(coor) abs(coor(:,1) - min(coor(:,1)))   < 1e-12;
+isRight  = @(coor) abs(coor(:,1) - max(coor(:,1)))   < 1e-12;
+isBottom = @(coor) abs(coor(:,2) - min(coor(:,2)))   < 1e-12;
+isTop    = @(coor) abs(coor(:,2) - max(coor(:,2)))   < 1e-12;
+
+dir_vel{1}.domain    = @(coor) isTop(coor);
+dir_vel{1}.direction = [1,2];
+dir_vel{1}.value     = [1,0];
+
+dir_vel{2}.domain    = @(coor) (isBottom(coor) | isRight(coor) | isLeft(coor)) & ~isTop(coor);
+dir_vel{2}.direction = [1,2];
+dir_vel{2}.value     = [0,0]; 
+
+dirichlet = [];
+dir_dofs  = [];
+for i = 1:length(dir_vel)
+    dirDofs = u.getDofsFromCondition(dir_vel{i}.domain);
+    dofs    = 1 + (dirDofs(2:2:end) - 2) / u.ndimf;
+    iNod    = repelem(dofs, 2)';
+    dofType = repmat((1:2)', length(dofs), 1);
+    valmat  = repmat(dir_vel{i}.value', length(dofs), 1);
+    dirichlet = [dirichlet; [iNod', dofType, valmat]];
+    dir_dofs  = [dir_dofs; dirDofs(:)];
+end
+
+% =========================================================================
+% 4) APPLIED BODY FORCES
+% =========================================================================
+sAF.fHandle = @(coor) [0.*coor, 0.*coor];
+sAF.ndimf   = 2;
+sAF.mesh    = mesh;
+forcesFormula = AnalyticalFunction(sAF);
+
+% =========================================================================
+% 5) BUILDING MATRICES FOR THE LINEAR STOKES PROBLEM
+% =========================================================================
+% -- Mass matrix (velocity)
+s1.type = 'MassMatrix'; s1.mesh = mesh; s1.test = u; s1.trial = u;
+M  = LHSIntegrator.create(s1).compute();
+M_lumped = spdiags(sum(M,2), 0, size(M,1), size(M,2));   % diagonal
+
+% -- Stiffness matrix (velocity)
+s2.type = 'StiffnessMatrix'; s2.mesh = mesh; s2.test = u; s2.trial = u;
+K = LHSIntegrator.create(s2).compute();
+
+% -- Divergence operator  B  (size n_dofs_u × n_dofs_p)
+s3.type = 'WeakDivergence'; s3.mesh = mesh; s3.trial = p; s3.test = u;
+B = LHSIntegrator.create(s3).compute();
+
+% -- Load vector  F  (velocity part only)
+s4.type = 'Stokes'; s4.mesh = mesh; s4.velocityFun = u;
+s4.pressureFun = p; s4.forcesFormula = forcesFormula;
+F = RHSIntegrator.create(s4).integrate();
+F = F(1:n_dofs_u);
+
+% -------------------------------------------------------------------------
+% PRE-COMPUTE bits for the matrix-free Schur complement
+% -------------------------------------------------------------------------
+pFix = 1;                               % pressure anchor DOF
+M_L_inv = 1 ./ full(diag(M_lumped));    % vector (n_dofs_u × 1)
+
+% handle that applies  S = B' * M_L_inv * B   without assembling S
+applyS = @(pvec) localSchur(pvec,B,M_L_inv,pFix);
+
+% Jacobi preconditioner   P ≈ diag(S)
+diagS = sum( (B.^2) .* M_L_inv , 1 )';   % column vector (n_dofs_p × 1)
+diagS(pFix)  = 1;                               % keep pin row SPD
+Minv = @(x) x ./ diagS;                 % function-handle M⁻¹x
+
+% =========================================================================
+% 6) FORWARD–BACKWARD (PROJECTION) ITERATION
+% =========================================================================
+maxIter  = 2e5;   tol = 1e-6;   lambda = 0.00001;
+u_k1     = zeros(n_dofs_u,1);
+p_k1     = zeros(n_dofs_p,1);
+
+for iter = 1:maxIter
+    % ---------------- velocity predictor ----------------
+    u_k = u_k1;
+    u_k(dir_dofs) = dirichlet(:,3);
+    u_ast = u_k - lambda*(K*u_k - F);
+
+    % ---------------- pressure solve  (Schur system) ----------------
+    rhs_p       = B' * u_ast;
+    rhs_p(pFix) = 0;                              % honour pinning
+
+    tol_p   = 1e-8;
+    max_pcg = 200;
+    [p_k1,flag,rel,its] = pcg(applyS, rhs_p, tol_p, max_pcg, Minv, [], p_k1);
+
+    if flag~=0
+        warning('PCG did not converge: flag %d, relres %.2e, it %d',flag,rel,its);
+    end
+
+    % ---------------- velocity corrector ----------------
+    u_k1 = u_ast - M_L_inv .* (B * p_k1);        % diag solve
+    u_k1(dir_dofs) = dirichlet(:,3);             % re-enforce BC
+
+    % ---------------- convergence check ----------------
+    step = norm(u_k1-u_k) / (norm(u_k)+eps);
+    if step < tol
+        fprintf('Converged in %d iterations, step = %.2e\n',iter,step);
+        break
+    end
+    if mod(iter,10)==0
+        fprintf('it %5d | step %.3e | PCG its %3d\n',iter,step,its);
+    end
+end
+
+% =========================================================================
+% 7) POST-PROCESSING & PLOTS
+% =========================================================================
+nu     = u.ndimf;
+nNode  = length(u_k1)/nu;
+nodes  = 1:nNode;
+velfval = zeros(nNode, nu);
+for idim = 1:nu
+    dofs = nu*(nodes-1) + idim;
+    velfval(:,idim) = u_k1(dofs);
+end
+u.setFValues(velfval);
+p.setFValues(p_k1);
+
+u.plot();
+p.plot();
+
+% Example velocity profile at x = 0.5
+mid_x   = 0.5;
+mid_idx = find(abs(mesh.coord(:,1) - mid_x) < 1e-3);
+figure;
+plot(mesh.coord(mid_idx,2), velfval(mid_idx,1), 'LineWidth', 2);
+xlabel('y'); ylabel('u-velocity'); title('u(y) at x = 0.5'); grid on;
+
+% Example velocity profile at y = 0.5
+mid_y   = 0.5;
+mid_idy = find(abs(mesh.coord(:,2) - mid_y) < 1e-3);
+figure;
+plot(mesh.coord(mid_idy,1), velfval(mid_idy,2), 'LineWidth', 2);
+xlabel('x'); ylabel('v-velocity'); title('v(x) at y = 0.5'); grid on;
+
+% -------------------------------------------------------------------------
+%  LOCAL FUNCTION: matrix-free Schur-complement operator
+% -------------------------------------------------------------------------
+function y = localSchur(pvec,B,M_L_inv,pFix)
+    y        = B' * (M_L_inv .* (B * pvec));  %  Bᵀ M_L⁻¹ B p
+    y(pFix)  = pvec(pFix);                    % enforce pin row (SPD)
+end
diff --git a/ns_pau_tarres/stokes/stokes_fbs_old.m b/ns_pau_tarres/stokes/stokes_fbs_old.m
new file mode 100644
index 0000000000..7e44f5a8e6
--- /dev/null
+++ b/ns_pau_tarres/stokes/stokes_fbs_old.m
@@ -0,0 +1,160 @@
+clear
+clc
+
+% =========================================================================
+% 1) CREATE MESH
+% =========================================================================
+mesh = UnitTriangleMesh(70,70);
+
+% =========================================================================
+% 2) CREATE FINITE ELEMENT FUNCTIONS (velocity u, pressure p)
+% =========================================================================
+u = LagrangianFunction.create(mesh, 2, 'P2');  % velocity
+p = LagrangianFunction.create(mesh, 1, 'P1');  % pressure
+n_dofs_u = u.nDofs;
+n_dofs_p = p.nDofs;
+n_dofs   = n_dofs_u + n_dofs_p;
+
+% =========================================================================
+% 3) SET UP BOUNDARY CONDITIONS (Dirichlet)
+% =========================================================================
+isLeft   = @(coor) abs(coor(:,1) - min(coor(:,1)))   < 1e-12;
+isRight  = @(coor) abs(coor(:,1) - max(coor(:,1)))   < 1e-12;
+isBottom = @(coor) abs(coor(:,2) - min(coor(:,2)))   < 1e-12;
+isTop    = @(coor) abs(coor(:,2) - max(coor(:,2)))   < 1e-12;
+
+dir_vel{1}.domain    = @(coor) isTop(coor);
+dir_vel{1}.direction = [1,2];
+dir_vel{1}.value     = [1,0];    % velocity on the top boundary
+
+dir_vel{2}.domain    = @(coor) isBottom(coor) | isRight(coor) | isLeft(coor);
+dir_vel{2}.direction = [1,2];
+dir_vel{2}.value     = [0,0];    % velocity = 0 elsewhere
+
+dirichlet = [];
+dir_dofs = [];
+for i = 1:length(dir_vel)
+    dirDofs = u.getDofsFromCondition(dir_vel{i}.domain);
+    dofs   = 1 + (dirDofs(2:2:end) - 2) / u.ndimf;
+    iNod    = repelem(dofs, 2)';
+    dofType = repmat((1:2)', length(dofs), 1);
+    valmat  = repmat(dir_vel{i}.value', length(dofs), 1);
+    dirichlet  = [dirichlet; [iNod', dofType, valmat]];
+    dir_dofs   = [dir_dofs; dirDofs(:)];
+end
+
+% =========================================================================
+% 4) APPLIED FORCES
+% =========================================================================
+sAF.fHandle = @(coor) [0.*coor, 0.*coor];
+sAF.ndimf   = 2;
+sAF.mesh    = mesh;
+forcesFormula = AnalyticalFunction(sAF);
+
+% =========================================================================
+% 5) BUILD MATRICES FOR THE LINEAR STOKES PROBLEM
+% =========================================================================
+% (a) Diffusion / stiffness matrix
+s1.type  = 'StiffnessMatrix';
+s1.mesh  = mesh;
+s1.test  = u;
+s1.trial = u;
+LHS1 = LHSIntegrator.create(s1);
+K = LHS1.compute();
+
+% (b) Divergence matrix
+s2.type  = 'WeakDivergence';
+s2.mesh  = mesh;
+s2.trial = p;
+s2.test  = u;
+LHS2 = LHSIntegrator.create(s2);
+D = LHS2.compute();
+
+% (c) Forces vector
+s3.type          = 'Stokes';
+s3.mesh          = mesh;
+s3.velocityFun   = u;
+s3.pressureFun   = p;
+s3.forcesFormula = forcesFormula;
+RHSint = RHSIntegrator.create(s3);
+f = RHSint.integrate();
+f_u = f(1:n_dofs_u);
+f_p = f((n_dofs_u+1):n_dofs);
+
+
+% =========================================================================
+% 6) FORWARD-BACKWARD ITERATION
+% =========================================================================
+maxIter = 1000;
+tol     = 1e-6;
+
+% Choose a step size λ < 2/L. We approximate the largest eigenvalue of LHS:
+lambda = 0.005;
+
+u_k1 = zeros(n_dofs_u, 1);
+p_k1 = zeros(n_dofs_p, 1);
+
+for iter = 1:maxIter
+    u_k = u_k1;
+    p_k = p_k1;
+
+    % (1) FORWARD STEP
+    grad_F = K*u_k - f_u;
+    u_half = u_k - lambda*grad_F;
+    
+    % (2) BACKWARD STEP (prox)
+    p_k1 = (D'*D)\( D'*u_half / lambda );
+    u_k1 = u_half - lambda*( D * p_k1 );
+
+    u_k1(dir_dofs) = dirichlet(:,3);
+
+
+    step_norm = norm(u_k1 - u_k) / (norm(u_k) + eps);
+    if step_norm < tol
+        fprintf('FBS converged at iteration %d, rel. step = %.3e\n',iter,step_norm);
+        break;
+    end
+
+    if mod(iter,50)==0
+        fprintf('Iter: %i\t StepNorm: %d\n', iter,step_norm)
+    end
+end
+
+% =========================================================================
+% 7) EXTRACT AND PLOT THE RESULTS
+% =========================================================================
+% Store velocity values in a matrix for post-processing
+nu    = u.ndimf;
+nNode = round(length(u_k1)/nu);
+nodes = 1:nNode;
+velfval = zeros(nNode, nu);
+for idim = 1:nu
+    dofs = nu*(nodes-1) + idim;
+    velfval(:,idim) = u_k1(dofs);
+end
+u.setFValues(velfval);
+p.setFValues(p_k1);
+
+% Plot velocity and pressure solutions
+u.plot();
+p.plot();
+
+% Example velocity profile at x=0.5
+mid_x = 0.5;
+mid_idx = find(abs(mesh.coord(:,1) - mid_x) < 1e-3);
+figure;
+plot(mesh.coord(mid_idx,2), velfval(mid_idx,1), 'LineWidth', 2);
+xlabel('y-coordinate');
+ylabel('u-velocity');
+title('Velocity Profile at x = 0.5');
+grid on;
+
+% Example velocity profile at y=0.5
+mid_y = 0.5;
+mid_idy = find(abs(mesh.coord(:,2) - mid_y) < 1e-3);
+figure;
+plot(mesh.coord(mid_idy,1), velfval(mid_idy,2), 'LineWidth', 2);
+xlabel('x-coordinate');
+ylabel('v-velocity');
+title('Velocity Profile at y = 0.5');
+grid on;
diff --git a/ns_pau_tarres/stokes/stokes_monolithic.m b/ns_pau_tarres/stokes/stokes_monolithic.m
new file mode 100644
index 0000000000..aa21d726d6
--- /dev/null
+++ b/ns_pau_tarres/stokes/stokes_monolithic.m
@@ -0,0 +1,148 @@
+clear
+clc
+
+% =========================================================================
+% 1) CREATE MESH
+% =========================================================================
+mesh = UnitTriangleMesh(100,100);
+
+% =========================================================================
+% 2) CREATE FINITE ELEMENT FUNCTIONS (velocity u, pressure p)
+% =========================================================================
+u = LagrangianFunction.create(mesh, 2, 'P2');
+p = LagrangianFunction.create(mesh, 1, 'P1');
+n_dofs = u.nDofs + p.nDofs;
+
+% =========================================================================
+% 3) SET UP BOUNDARY CONDITIONS (Dirichlet)
+% =========================================================================
+isLeft   = @(coor) (abs(coor(:,1) - min(coor(:,1)))   < 1e-12);
+isRight  = @(coor) (abs(coor(:,1) - max(coor(:,1)))   < 1e-12);
+isBottom = @(coor) (abs(coor(:,2) - min(coor(:,2)))   < 1e-12);
+isTop    = @(coor) (abs(coor(:,2) - max(coor(:,2)))   < 1e-12);
+
+dir_vel{1}.domain    = @(coor) isTop(coor);
+dir_vel{1}.direction = [1,2];
+dir_vel{1}.value     = [1,0];
+
+dir_vel{2}.domain    = @(coor) (isBottom(coor) | isRight(coor) | isLeft(coor)) & not(isTop(coor));
+dir_vel{2}.direction = [1,2];
+dir_vel{2}.value     = [0,0]; 
+
+dirichlet = [];
+dir_dofs = [];
+for i = 1:length(dir_vel)
+    dirDofs = u.getDofsFromCondition(dir_vel{i}.domain);
+    nodes = 1 + (dirDofs(2:2:end) - 2) / u.ndimf;
+    iNod = repelem(nodes, 2)';
+    dofType = repmat((1:2)', length(nodes), 1);
+    valmat = repmat(dir_vel{i}.value', length(nodes), 1);
+    dirichlet = [dirichlet; [iNod', dofType, valmat]];
+    dir_dofs = [dir_dofs; dirDofs(:)];
+end
+
+% =========================================================================
+% 4) APPLIED FORCES
+% =========================================================================
+sAF.fHandle = @(coor) [0.*coor,0.*coor];
+sAF.ndimf   = 2;
+sAF.mesh    = mesh;
+forcesFormula = AnalyticalFunction(sAF);
+
+% =========================================================================
+% 5) BUILD MATRICES FOR THE LINEAR STOKES PROBLEM
+% =========================================================================
+% (a) Diffusion / stiffness matrix
+s1.type  = 'StiffnessMatrix';
+s1.mesh  = mesh;
+s1.test  = u;
+s1.trial = u;
+LHS1 = LHSIntegrator.create(s1);
+K = LHS1.compute();
+
+% (b) Divergence matrix
+s2.type = 'WeakDivergence';
+s2.mesh = mesh;
+s2.trial = p;
+s2.test  = u;
+LHS2 = LHSIntegrator.create(s2);
+D = LHS2.compute();
+
+% (c) Forces vector
+s3.type          = 'Stokes';
+s3.mesh          = mesh;
+s3.velocityFun   = u;
+s3.pressureFun   = p;
+s3.forcesFormula = forcesFormula;
+RHSint = RHSIntegrator.create(s3);
+f = RHSint.integrate();
+
+% C
+n_dir = length(dir_dofs);
+C = sparse(dir_dofs, 1:n_dir, 1, u.nDofs, n_dir);
+
+% 0
+O1 = zeros(p.nDofs);
+O2 = zeros(p.nDofs, n_dir);
+O3 = zeros(n_dir);
+O4 = zeros(p.nDofs, 1);
+
+
+% =========================================================================
+% 6) SOLVE SYSTEM
+% =========================================================================
+LHS = [K D C; D' O1 O2; C' O2' O3];
+RHS = [f; dirichlet(:,3)];
+
+pFix = 1;
+LHS(pFix + u.nDofs, :) = 0;
+LHS(:, pFix + u.nDofs) = 0;
+LHS(pFix + u.nDofs, pFix + u.nDofs) = 1;
+RHS(pFix + u.nDofs) = 0;
+
+fullx = LHS\RHS;
+U = fullx(1:u.nDofs);
+P = fullx((1:p.nDofs)+u.nDofs);
+
+% =========================================================================
+% 7) EXTRACT AND PLOT THE RESULTS
+% =========================================================================
+% SEPARATE VARIABLES FVALUES
+vars.u = U;
+vars.p = P;
+
+% DEFINE VARIABLES
+nu = u.ndimf;
+nnode = round(length(vars.u)/nu);
+nodes = 1:nnode;
+velfval = zeros(nnode,nu);
+for idim = 1:nu
+    dofs = nu*(nodes-1)+idim;
+    velfval(:,idim) = vars.u(dofs, end);
+end
+u.setFValues(velfval)
+p.setFValues(vars.p(:,end))
+
+% PLOT RESULTS
+u.plot();
+p.plot();
+
+% Example: velocity profile at x=0.5
+mid_x = 0.5;
+mid_idx = find(abs(mesh.coord(:,1) - mid_x) < 1e-3);
+figure;
+plot(mesh.coord(mid_idx,2), velfval(mid_idx,1), 'LineWidth', 2);
+xlabel('y-coordinate');
+ylabel('u-velocity');
+title('Velocity Profile at x = 0.5');
+grid on;
+
+% Example: velocity profile at y=0.5
+mid_y = 0.5;
+mid_idy = find(abs(mesh.coord(:,2) - mid_y) < 1e-3);
+figure;
+plot(mesh.coord(mid_idy,1), velfval(mid_idy,2), 'LineWidth', 2);
+xlabel('x-coordinate');
+ylabel('v-velocity');
+title('Velocity Profile at y = 0.5');
+grid on;
diff --git a/results_fem.vtu b/results_fem.vtu
deleted file mode 100644
index bee7dc570c..0000000000
--- a/results_fem.vtu
+++ /dev/null
@@ -1,89 +0,0 @@
-<?xml version="1.0" encoding="utf-8"?>
-<VTKFile byte_order="LittleEndian" type="UnstructuredGrid" version="0.1">
-   <UnstructuredGrid>
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-0.0200 0.0000 0.0000
-0.0200 0.0200 0.0000
-0.0100 0.0300 0.0000
-0.0300 0.0100 0.0000
-0.0000 0.0400 0.0000
-0.0400 0.0000 0.0000
-0.0300 0.0300 0.0000
-0.0400 0.0200 0.0000
-0.0200 0.0400 0.0000
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- 2 1 4
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--2.87861e-17  1.15144e-16        00000 
--1.85906e+00 -2.44576e+00        00000 
-       00000 -2.07997e+00        00000 
- 4.19043e-01 -8.99050e-01        00000 
--1.18498e+00 -3.92680e+00        00000 
- 7.19653e-18 -1.79018e-16        00000 
--2.40092e+00 -5.42913e+00        00000 
- 1.18498e+00 -3.92680e+00        00000 
- 2.86853e-17 -6.02324e+00        00000 
- 1.85906e+00 -2.44576e+00        00000 
- 2.40092e+00 -5.42913e+00        00000 </DataArray>
-            <DataArray Name="strain" NumberOfComponents="4" format="ascii" type="Float64">
--9.08538e+01 -4.86196e+01 -4.86196e+01  2.10125e+01 
--5.24722e+01 -2.95819e+01 -2.95819e+01  3.33153e+00 
- 7.70158e-14 -4.12854e+01 -4.12854e+01  1.93342e-14 
--7.10703e+01 -2.73605e+01 -2.73605e+01  3.88188e+01 
--3.32434e-14 -3.10736e+01 -3.10736e+01  1.26325e-14 
- 5.24722e+01 -2.95819e+01 -2.95819e+01 -3.33153e+00 
--7.55079e+00 -3.70848e+01 -3.70848e+01 -1.31824e+01 
- 9.08538e+01 -4.86196e+01 -4.86196e+01 -2.10125e+01 
--7.09739e+00 -2.25665e+01 -2.25665e+01 -3.17539e+01 
- 7.55079e+00 -3.70848e+01 -3.70848e+01  1.31824e+01 
- 1.19331e-14 -3.73270e+01 -3.73270e+01 -1.34018e-13 
- 7.10703e+01 -2.73605e+01 -2.73605e+01 -3.88188e+01 
- 7.09739e+00 -2.25665e+01 -2.25665e+01  3.17539e+01 </DataArray>
-            <DataArray Name="stress" NumberOfComponents="4" format="ascii" type="Float64">
--9.43308e+01 -3.64647e+01 -3.64647e+01 -1.04311e+01 
--5.77819e+01 -2.21864e+01 -2.21864e+01 -1.59291e+01 
- 9.12146e-14 -3.09640e+01 -3.09640e+01  4.27810e-14 
--6.53971e+01 -2.05203e+01 -2.05203e+01  1.70197e+01 
--2.52650e-14 -2.33052e+01 -2.33052e+01  5.31895e-15 
- 5.77819e+01 -2.21864e+01 -2.21864e+01  1.59291e+01 
--1.34380e+01 -2.78136e+01 -2.78136e+01 -1.76617e+01 
- 9.43308e+01 -3.64647e+01 -3.64647e+01  1.04311e+01 
--1.98923e+01 -1.69249e+01 -1.69249e+01 -3.83846e+01 
- 1.34380e+01 -2.78136e+01 -2.78136e+01  1.76617e+01 
--3.57992e-14 -2.79953e+01 -2.79953e+01 -1.45262e-13 
- 6.53971e+01 -2.05203e+01 -2.05203e+01 -1.70197e+01 
- 1.98923e+01 -1.69249e+01 -1.69249e+01  3.83846e+01 </DataArray>
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-         <CellData/>
-      </Piece>
-   </UnstructuredGrid>
-</VTKFile>
\ No newline at end of file
diff --git a/results_fem_disp.flavia.msh b/results_fem_disp.flavia.msh
deleted file mode 100644
index f1f3e0a093..0000000000
--- a/results_fem_disp.flavia.msh
+++ /dev/null
@@ -1,41 +0,0 @@
-####################################################
-################# FEM-MAT-OO v.1.0 #################
-####################################################
-
-MESH "WORKPIECE" dimension   2   Elemtype Triangle   Nnode  3 
- 
-coordinates 
-     1        00000        00000 
-     2  1.00000e-02  1.00000e-02 
-     3        00000  2.00000e-02 
-     4  2.00000e-02        00000 
-     5  2.00000e-02  2.00000e-02 
-     6  1.00000e-02  3.00000e-02 
-     7  3.00000e-02  1.00000e-02 
-     8        00000  4.00000e-02 
-     9  4.00000e-02        00000 
-    10  3.00000e-02  3.00000e-02 
-    11  4.00000e-02  2.00000e-02 
-    12  2.00000e-02  4.00000e-02 
-    13  4.00000e-02  4.00000e-02 
-end coordinates 
- 
-elements 
-     1      5      2      4  1 
-     2      3      2      5  1 
-     3      1      2      3  1 
-     4      4      2      1  1 
-     5     12      6      5  1 
-     6      8      6     12  1 
-     7      3      6      8  1 
-     8      5      6      3  1 
-     9     11      7      9  1 
-    10      5      7     11  1 
-    11      4      7      5  1 
-    12      9      7      4  1 
-    13     13     10     11  1 
-    14     12     10     13  1 
-    15      5     10     12  1 
-    16     11     10      5  1 
-end elements
-
diff --git a/results_fem_disp.flavia.res b/results_fem_disp.flavia.res
deleted file mode 100644
index 17da0e5ac3..0000000000
--- a/results_fem_disp.flavia.res
+++ /dev/null
@@ -1,26 +0,0 @@
-GiD Post Results File 1.0 
-GaussPoints "Gauss Points" Elemtype Triangle
-Number of Gauss Points: 1 
-Nodes not included 
-Natural Coordinates: given 
- 3.33333e-01  3.33333e-01 
-End GaussPoints  
-
-Result "fValues" "FunResults" 0 Vector OnNodes 
-ComponentNames  "x1", "x2"
-Values  
- 1        00000        00000 
- 2 -4.19043e-01 -8.99050e-01 
- 3        00000        00000 
- 4 -1.85906e+00 -2.44576e+00 
- 5  1.20854e-16 -2.07997e+00 
- 6  4.19043e-01 -8.99050e-01 
- 7 -1.18498e+00 -3.92680e+00 
- 8        00000        00000 
- 9 -2.40092e+00 -5.42913e+00 
-10  1.18498e+00 -3.92680e+00 
-11  5.73757e-17 -6.02324e+00 
-12  1.85906e+00 -2.44576e+00 
-13  2.40092e+00 -5.42913e+00 
-End Values
-
diff --git a/results_fem_disp.vtu b/results_fem_disp.vtu
deleted file mode 100644
index 017a518b05..0000000000
--- a/results_fem_disp.vtu
+++ /dev/null
@@ -1,61 +0,0 @@
-<?xml version="1.0" encoding="utf-8"?>
-<VTKFile byte_order="LittleEndian" type="UnstructuredGrid" version="0.1">
-   <UnstructuredGrid>
-      <Piece NumberOfCells="16" NumberOfPoints="13">
-         <Points>
-            <DataArray Name="Points" NumberOfComponents="3" format="ascii" type="Float32">
-0.0000 0.0000 0.0000
-0.0100 0.0100 0.0000
-0.0000 0.0200 0.0000
-0.0200 0.0000 0.0000
-0.0200 0.0200 0.0000
-0.0100 0.0300 0.0000
-0.0300 0.0100 0.0000
-0.0000 0.0400 0.0000
-0.0400 0.0000 0.0000
-0.0300 0.0300 0.0000
-0.0400 0.0200 0.0000
-0.0200 0.0400 0.0000
-0.0400 0.0400 0.0000</DataArray>
-         </Points>
-         <Cells>
-            <DataArray Name="connectivity" format="ascii" type="Int32">
- 4 1 3
- 2 1 4
- 0 1 2
- 3 1 0
- 11 5 4
- 7 5 11
- 2 5 7
- 4 5 2
- 10 6 8
- 4 6 10
- 3 6 4
- 8 6 3
- 12 9 10
- 11 9 12
- 4 9 11
- 10 9 4</DataArray>
-            <DataArray Name="offsets" format="ascii" type="Int32">3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 </DataArray>
-            <DataArray Name="types" format="ascii" type="UInt8">5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 </DataArray>
-         </Cells>
-         <PointData>
-            <DataArray Name="fValues" NumberOfComponents="3" format="ascii" type="Float64">
- 1.50231e-16 -3.00463e-16        00000 
--4.19043e-01 -8.99050e-01        00000 
--2.87861e-17  1.15144e-16        00000 
--1.85906e+00 -2.44576e+00        00000 
-       00000 -2.07997e+00        00000 
- 4.19043e-01 -8.99050e-01        00000 
--1.18498e+00 -3.92680e+00        00000 
- 7.19653e-18 -1.79018e-16        00000 
--2.40092e+00 -5.42913e+00        00000 
- 1.18498e+00 -3.92680e+00        00000 
- 2.86853e-17 -6.02324e+00        00000 
- 1.85906e+00 -2.44576e+00        00000 
- 2.40092e+00 -5.42913e+00        00000 </DataArray>
-         </PointData>
-         <CellData/>
-      </Piece>
-   </UnstructuredGrid>
-</VTKFile>
\ No newline at end of file
diff --git a/src/Functions/FEFunctions/Interpolation/LineConstant.m b/src/Functions/FEFunctions/Interpolation/LineConstant.m
index abae8296d1..3a54ed089b 100644
--- a/src/Functions/FEFunctions/Interpolation/LineConstant.m
+++ b/src/Functions/FEFunctions/Interpolation/LineConstant.m
@@ -4,17 +4,26 @@
 
         function obj = LineConstant(cParams)
             obj.init(cParams);
-            obj.computeParams();
         end
-        
-        function shape = computeShapeFunctions(obj,posgp)
+
+    end
+
+    methods (Access = protected)
+
+        function computeParams(obj)
+            obj.ndime = 1;
+            obj.nnode = 1;
+            obj.pos_nodes = [0 0];
+        end
+
+        function shape = evaluateShapeFunctions(obj,posgp)
             ngaus = length(posgp);
             nelem = size(posgp,3);
             N = ones(obj.nnode,ngaus, nelem);
             shape = N;
         end
-        
-        function deriv = computeShapeDerivatives(obj,posgp)
+
+        function deriv = evaluateShapeDerivatives(obj,posgp)
             ngaus = length(posgp);
             nelem = size(posgp,3);
             dN = zeros(obj.ndime,ngaus, nelem);
@@ -23,15 +32,4 @@
 
     end
 
-    methods (Access = private)
-
-        function computeParams(obj)
-            obj.type = 'LINE';
-            obj.ndime = 2;
-            obj.nnode = 1;
-            obj.pos_nodes = [0 0];
-        end
-        
-    end
-    
 end
\ No newline at end of file
diff --git a/src/Functions/FEFunctions/LagrangianFunction.m b/src/Functions/FEFunctions/LagrangianFunction.m
index 26540645da..d93e22119b 100644
--- a/src/Functions/FEFunctions/LagrangianFunction.m
+++ b/src/Functions/FEFunctions/LagrangianFunction.m
@@ -3,11 +3,12 @@
     properties (GetAccess = public, SetAccess = private)
         nDofs
         nDofsElem
+        dofCoord
     end
 
     properties (Access = private)
         interpolation
-        dofCoord
+        
         dofConnec
 
        dNdxOld
@@ -79,7 +80,7 @@ function setFValues(obj,fV)
                 dNdx = obj.dNdxOld;
             end
         end         
-
+        
        function fVals = getFvaluesByElem(obj)
             nDimF     = obj.ndimf;
             nNode     = obj.interpolation.nnode;
@@ -204,9 +205,13 @@ function plotVector(obj,varargin) %only for linear
         function dof = getDofsFromCondition(obj, condition)
             nodes = condition(obj.dofCoord);
             iNode = find(nodes==1);
-            dofElem = repmat(1:obj.ndimf, [length(iNode) 1]);
-            dofMat = obj.ndimf*(iNode - 1) + dofElem;
-            dof = sort(dofMat(:));
+            dof   = iNode;
+
+            if strcmp(obj.order, 'P2')
+                dofElem = repmat(1:obj.ndimf, [length(iNode) 1]);
+                dofMat = obj.ndimf*(iNode - 1) + dofElem;
+                dof = sort(dofMat(:));
+            end
         end
 
         function print(obj, filename, software)
@@ -490,7 +495,10 @@ function plotF(obj,tri,x,y,z,iDim)
             a = trisurf(tri,x,y,z);
             view(0,90)
             %colorbar
-            shading interp
+            if not(size(tri,2) == 2)
+                shading interp
+                a.EdgeAlpha = 0;
+            end
             a.EdgeColor = [0 0 0];
             title(['dim = ', num2str(iDim)]);
         end
diff --git a/src/Integrators/LHS/LHSIntegratorConvective.m b/src/Integrators/LHS/LHSIntegratorConvective.m
new file mode 100644
index 0000000000..de363a12de
--- /dev/null
+++ b/src/Integrators/LHS/LHSIntegratorConvective.m
@@ -0,0 +1,65 @@
+classdef LHSIntegratorConvective < LHSIntegrator
+
+    methods (Access = public)
+
+        function obj = LHSIntegratorConvective(cParams)
+            obj@LHSIntegrator(cParams)
+        end
+
+        function [LHS, u] = compute(obj, velocityField)
+            [lhs, u] = obj.computeElementalLHS(velocityField);
+            LHS = obj.assembleMatrix(lhs);
+        end
+
+    end
+
+    methods (Access = private)
+
+        function [lhs, uValues] = computeElementalLHS(obj,velocityField)
+            xV          = obj.quadrature.posgp;  
+            NTest       = obj.test.computeShapeFunctions(xV);
+            dNdxTest    = obj.test.evaluateCartesianDerivatives(xV);
+            dNdxTrial   = obj.trial.evaluateCartesianDerivatives(xV);
+            dVolu       = obj.mesh.computeDvolume(obj.quadrature);            
+
+            nGaus       = obj.quadrature.ngaus;
+            nElem       = size(dVolu, 2);
+
+            nNodeTest   = size(dNdxTest, 2);
+            nNodeTrial  = size(dNdxTrial, 2);
+            nDofTest    = nNodeTest * obj.test.ndimf;
+            nDofTrial   = nNodeTrial * obj.trial.ndimf;
+
+            lhs = zeros(nDofTest, nDofTrial, nElem);
+            uValues = velocityField.evaluate(xV);
+
+            
+            for iGaus = 1:nGaus
+                uGp = squeeze(uValues(:, iGaus, :));  % [nDim x nElem]
+                dV   = dVolu(iGaus, :);                % [1 x nElem]
+            
+                for iNode = 1:nNodeTest
+                    phiI = NTest(iNode, iGaus);        % scalar
+            
+                    for jNode = 1:nNodeTrial
+                        gradPhiJ = squeeze(dNdxTrial(:, jNode, iGaus, :)); % [nDim x nElem]
+            
+                        for iDim = 1:obj.test.ndimf
+                            idof = obj.test.ndimf * (iNode - 1) + iDim;
+            
+                            for jDim = 1:obj.trial.ndimf
+                                jdof = obj.trial.ndimf * (jNode - 1) + jDim;
+                                convTerm = uGp(jDim, :) .* gradPhiJ(jDim, :);  % [1 x nElem]
+            
+                                % update matrix entry
+                                lhs(idof, jdof, :) = lhs(idof, jdof, :) + ...
+                                    reshape(phiI * convTerm .* dV, [1 1 nElem]);
+                            end
+                        end
+                    end
+                end
+            end
+        end
+
+    end
+end
\ No newline at end of file
diff --git a/src/Integrators/LHS/LHSIntegratorDobleWeakDivergence.m b/src/Integrators/LHS/LHSIntegratorDobleWeakDivergence.m
new file mode 100644
index 0000000000..ccfb5e0e47
--- /dev/null
+++ b/src/Integrators/LHS/LHSIntegratorDobleWeakDivergence.m
@@ -0,0 +1,93 @@
+classdef LHSIntegratorDobleWeakDivergence < handle
+
+    properties (Access = private)
+        trial
+        test
+        mesh
+        quadrature
+    end
+
+    methods (Access = public)
+
+        function obj = LHSIntegratorDobleWeakDivergence(cParams)
+            obj.init(cParams);
+            obj.createQuadrature();
+        end
+
+        function LHS = compute(obj)
+            lhs = obj.computeElementalLHS();
+            LHS = obj.assembleMatrix(lhs);
+        end
+
+    end
+
+    methods (Access = protected)
+
+        function lhs = computeElementalLHS(obj)
+            xV = obj.quadrature.posgp;
+            dNdxTe = obj.test.evaluateCartesianDerivatives(xV);
+            dNdxTr = obj.trial.evaluateCartesianDerivatives(xV);
+            dvol = obj.mesh.computeDvolume(obj.quadrature)';  % [nElem x nGauss]
+
+            nElem  = obj.mesh.nelem;
+            nDim   = size(dNdxTe,1);
+            nNodeT = size(dNdxTe,2);
+            nNodeR = size(dNdxTr,2);
+            nGauss = size(dNdxTe,3);
+
+            nDofTest  = nNodeT * nDim;
+            nDofTrial = nNodeR * nDim;
+
+            lhs = zeros(nDofTest, nDofTrial, nElem);
+
+            for igaus = 1:nGauss
+                for inodeT = 1:nNodeT
+                    div_v = zeros(nElem,1);
+                    for idim = 1:nDim
+                        div_v = div_v + squeeze(dNdxTe(idim,inodeT,igaus,:));
+                    end
+                    for inodeR = 1:nNodeR
+                        div_w = zeros(nElem,1);
+                        for jdim = 1:nDim
+                            div_w = div_w + squeeze(dNdxTr(jdim,inodeR,igaus,:));
+                        end
+                        val = div_v .* div_w .* dvol(:,igaus);
+                        % Assign to all combinations of dof_test and dof_trial
+                        for idim = 1:nDim
+                            dof_test = (inodeT - 1)*nDim + idim;
+                            for jdim = 1:nDim
+                                dof_trial = (inodeR - 1)*nDim + jdim;
+                                lhs(dof_test, dof_trial, :) = squeeze(lhs(dof_test, dof_trial, :)) + val;
+                            end
+                        end
+                    end
+                end
+            end
+        end
+
+    end
+
+    methods (Access = private)
+
+        function init(obj, cParams)
+            obj.mesh  = cParams.mesh;
+            obj.trial = cParams.trial;
+            obj.test  = cParams.test;
+        end
+
+        function createQuadrature(obj)
+            orderTr = obj.trial.getOrderNum();
+            orderTe = obj.test.getOrderNum();
+            order = orderTr + orderTe;
+            obj.quadrature = Quadrature.create(obj.mesh, order);
+        end
+
+        function LHS = assembleMatrix(obj, lhs)
+            s.fun = []; % Placeholder
+            assembler = AssemblerFun(s);
+            LHS = assembler.assemble(lhs, obj.test, obj.trial);
+        end
+
+    end
+
+end
diff --git a/src/Integrators/LHS/LHSIntegratorFactory.m b/src/Integrators/LHS/LHSIntegratorFactory.m
index 9652816685..8e20895394 100644
--- a/src/Integrators/LHS/LHSIntegratorFactory.m
+++ b/src/Integrators/LHS/LHSIntegratorFactory.m
@@ -36,10 +36,14 @@
                    obj = LHSIntegratorStiffnessMass(cParams);
                case 'Stokes'
                    obj = LHSIntegratorStokes(cParams);
+               case 'NavierStokes'
+                   obj = LHSIntegratorNavierStokes(cParams);   
                case 'Laplacian'
                    obj = LHSIntegratorLaplacian(cParams);
                case 'WeakDivergence'
                    obj = LHSIntegratorWeakDivergence(cParams);
+               case 'Convective'
+                   obj = LHSIntegratorConvective(cParams);    
                case 'AdvectionMatrix'
                    obj = LHSIntegrator_Advection(cParams);                   
                case 'StiffnessMatrixWithFunction'
@@ -54,6 +58,10 @@
                    obj = LHSIntegratorFunctionAdvection(cParams); 
                case 'DivergenceMatrix'
                    obj = LHSintegratorDivergenceMatrix(cParams); 
+               case 'DobleDivergenceMatrix'
+                   obj = LHSIntegratorDobleWeakDivergence(cParams);
+               case 'NonLinearNS'
+                   obj = LHSintegrator_NonLinearNS(cParams);
            end
        end
    end
diff --git a/src/Integrators/LHS/LHSIntegratorFunctionStiffness.m b/src/Integrators/LHS/LHSIntegratorFunctionStiffness.m
index b5eb5b8a2c..242febd28a 100644
--- a/src/Integrators/LHS/LHSIntegratorFunctionStiffness.m
+++ b/src/Integrators/LHS/LHSIntegratorFunctionStiffness.m
@@ -29,7 +29,7 @@
             nElem = size(dVolu,2);
 
             nNodETs = size(dNdxTs,2);
-            nDofETs = nNodETs*obj.trial.ndimf;
+            nDofETs = nNodETs*obj.test.ndimf;
             nNodETr = size(dNdxTr,2);
             nDofETr = nNodETr*obj.trial.ndimf;
             lhs = zeros(nDofETs,nDofETr,nElem);
@@ -39,16 +39,18 @@
                 for inode= 1:nNodETs
                     for jnode= 1:nNodETr
                         for iunkn= 1:obj.test.ndimf
-                            for idim = 1:obj.mesh.ndim
-                                idof = obj.fun.ndimf*(inode-1)+iunkn;
-                                jdof = obj.fun.ndimf*(jnode-1)+iunkn;
-                                dvol = dVolu(iGaus,:);
-                                dNi = squeeze(dNdxTs(idim,inode,iGaus,:));
-                                dNj = squeeze(dNdxTr(idim,jnode,iGaus,:));
-                                fVG = squeeze(fV(1,iGaus,:));
-                                v = squeeze(fVG.*dNi.*dNj);
-                                lhs(idof, jdof, :)= squeeze(lhs(idof,jdof,:)) ...
-                                    + v(:).*dvol';
+                            for junkn= 1:obj.trial.ndimf
+                                for idim = 1:obj.mesh.ndim
+                                    idof = obj.test.ndimf*(inode-1)+iunkn;
+                                    jdof = obj.trial.ndimf*(jnode-1)+junkn;
+                                    dvol = dVolu(iGaus,:);
+                                    dNi = squeeze(dNdxTs(idim,inode,iGaus,:));
+                                    dNj = squeeze(dNdxTr(idim,jnode,iGaus,:));
+                                    fVG = squeeze(fV(1,iGaus,:));
+                                    v = squeeze(fVG.*dNi.*dNj);
+                                    lhs(idof, jdof, :)= squeeze(lhs(idof,jdof,:)) ...
+                                        + v(:).*dvol';
+                                end
                             end
                         end
                     end
diff --git a/src/Integrators/LHS/LHSIntegratorNavierStokePer.m b/src/Integrators/LHS/LHSIntegratorNavierStokePer.m
new file mode 100644
index 0000000000..56c6a6c6cc
--- /dev/null
+++ b/src/Integrators/LHS/LHSIntegratorNavierStokePer.m
@@ -0,0 +1,110 @@
+classdef LHSIntegratorNavierStokePer < handle
+
+    properties (GetAccess = public, SetAccess = private)
+        M
+    end
+
+    properties (Access = private)
+        dt
+        mesh
+        velocityFun
+        pressureFun
+        velocityField
+        material
+        D
+    end
+
+    methods (Access = public)
+
+        function obj = LHSIntegratorNavierStokePer(cParams)
+            obj.init(cParams);
+        end
+
+        function LHS = compute(obj)
+            velLHS = obj.computeVelocityLHS();
+            D      = obj.computeWeakDivergenceMatrix();
+            prsLHS = obj.computePressureLHS(D);
+            LHS = [velLHS, D; D',prsLHS];
+        end
+
+        function C = computeConvectiveTerm(obj)
+            C = obj.computeConvectiveMatrix(obj);
+        end
+
+    end
+
+    methods (Access = private)
+    
+        function init(obj, cParams)
+            obj.dt            = cParams.dt;
+            obj.mesh          = cParams.mesh;
+            obj.material      = cParams.material;
+            obj.pressureFun   = cParams.pressureFun;
+            obj.velocityFun   = cParams.velocityFun;
+            obj.velocityField = cParams.velocityField;
+        end
+
+        function LHS = computeVelocityLHS(obj)
+            K   = obj.computeVelocityLaplacian();
+            M   = obj.computeMassMatrix();
+            lhs = obj.symGradient(K + M);
+            C   = obj.computeConvectiveMatrix();
+            LHS = lhs + C;
+        end
+
+        function D = computeWeakDivergenceMatrix(obj)
+            s.type = 'WeakDivergence';
+            s.mesh = obj.mesh;
+            s.trial = obj.pressureFun;
+            s.test  = obj.velocityFun;
+            LHS = LHSIntegrator.create(s);
+            D = LHS.compute();
+        end
+
+        function BB = computePressureLHS(obj,D)
+            sz = size(D, 2);
+            BB = sparse(sz,sz);
+        end
+
+        function A = symGradient(obj, B)
+            A = 1/2 * (B+B');
+        end
+
+        function lhs = computeVelocityLaplacian(obj)
+            s.type  = 'Laplacian';
+            s.mesh  = obj.mesh;
+            s.test  = obj.velocityFun;
+            s.trial = obj.velocityFun;
+            s.material = obj.material;
+            LHS = LHSIntegrator.create(s);
+            lhs = LHS.compute();
+            lhs = obj.symGradient(lhs);
+        end
+
+        function c = computeConvectiveMatrix(obj)
+            s.type  = 'Convective';
+            s.mesh  = obj.mesh;
+            s.test  = obj.velocityFun;
+            s.trial = obj.velocityFun;
+            s.material = obj.material;
+            C = LHSIntegrator.create(s);
+            c = C.compute(obj.velocityField);
+        end
+
+        function M = computeMassMatrix(obj)
+            s.type  = 'MassMatrix';
+            s.mesh  = obj.mesh;
+            s.test  = obj.velocityFun;
+            s.trial = obj.velocityFun;
+            s.quadratureOrder = 3;
+            LHS = LHSIntegrator.create(s);
+            m = LHS.compute();
+
+            dtime = obj.dt;
+            M = m/dtime;
+            obj.M = M;
+        end
+
+    end
+
+end
\ No newline at end of file
diff --git a/src/Integrators/LHS/LHSIntegratorNavierStokes.m b/src/Integrators/LHS/LHSIntegratorNavierStokes.m
new file mode 100644
index 0000000000..8a609e015a
--- /dev/null
+++ b/src/Integrators/LHS/LHSIntegratorNavierStokes.m
@@ -0,0 +1,233 @@
+classdef LHSIntegratorNavierStokes < handle
+
+    properties (Access = private)
+        mesh
+        velocityFun
+        pressureFun
+        velocityField
+        LHSS
+        dt
+        residual
+        nu
+    end
+
+    methods (Access = public)
+
+        function obj = LHSIntegratorNavierStokes(cParams)
+            obj.init(cParams);
+        end
+
+        function LHS = compute(obj)
+            [C, ~] = obj.computeConvectiveMatrix();
+            LHS = obj.addCMToLHS(C);
+        end
+
+        function LHS = computeStabilization(obj)
+            [C , a]   = obj.computeConvectiveMatrix();
+            Kvva2   = obj.computeVVA2Mat();
+            Kavp    = obj.computeAVPMat();
+            Kpva    = Kavp';
+            Kpp     = obj.computePPMat();
+            Kpdv    = obj.computePDivergenceVMatrix();
+            Kdvdv   = obj.computeVDVDMatrix();
+            tauS1 = obj.computeTauS1(C, Kvva2);
+            tauS3 = obj.computeTauS3(tauS1, a);
+            tauS   = obj.computeTau(tauS1,tauS3);
+            tauP1 = obj.computeTauS1(Kpdv, Kpva);
+            tauP3 = obj.computeTauP3(tauP1, a, tauS1);
+            tauP   = obj.computeTau(tauP1,tauP3);
+            tauL   = obj.computeTauS1(C,Kdvdv);
+            LHS   = obj.addTermsToLHS(C, tauS, Kvva2, Kavp, tauP, Kpva, Kpp, tauL, Kdvdv);
+        end
+
+
+
+        function [C , a] = computeConvectiveTermAndVelocityF(obj)
+            [C , a]  = obj.computeConvectiveMatrix();
+        end
+
+        function [M,D,KU,KP] = computeLHSMatrix(obj)
+            M  = obj.computeMassMatrix();
+            D  = obj.computeWeakDivergenceMatrix();
+            KU = obj.computeVelocityLaplacian();
+            KP = obj.computePressureMatrix();
+        end
+
+    end
+
+    methods (Access = private)
+
+        function init(obj, cParams)
+            obj.mesh          = cParams.mesh;
+            obj.velocityFun   = cParams.velocityFun;
+            obj.pressureFun   = cParams.pressureFun;
+            obj.velocityField = cParams.velocityField;
+            obj.LHSS          = cParams.LHSS;
+            obj.dt            = cParams.dt;
+            obj.residual      = cParams.residual;
+            obj.nu            = cParams.nu;
+        end
+
+        function [c,a] = computeConvectiveMatrix(obj)
+            s.type  = 'Convective';
+            s.mesh  = obj.mesh;
+            s.test  = obj.velocityFun;
+            s.trial = obj.velocityFun;
+            C = LHSIntegrator.create(s);
+            [c,a] = C.compute(obj.velocityField);
+        end
+
+        function D = computeWeakDivergenceMatrix(obj)
+            s.type = 'WeakDivergence';
+            s.mesh = obj.mesh;
+            s.trial = obj.pressureFun;
+            s.test  = obj.velocityFun;
+            LHS = LHSIntegrator.create(s);
+            D = LHS.compute();
+        end
+
+        function D = computePDivergenceVMatrix(obj)
+            s.type = 'WeakDivergence';
+            s.mesh = obj.mesh;
+            s.trial = obj.pressureFun;
+            s.test  = obj.velocityFun;
+            LHS     = LHSIntegrator.create(s);
+            D       = LHS.compute();
+            D       = - D';
+        end
+
+        function DD = computeVDVDMatrix(obj)
+            s.type = 'DobleDivergenceMatrix';
+            s.mesh = obj.mesh;
+            s.trial = obj.velocityFun;
+            s.test  = obj.velocityFun;
+            LHS     = LHSIntegrator.create(s);
+            DD       = - LHS.compute();
+        end
+
+        function lhs = computeVelocityLaplacian(obj)
+            n       = obj.nu;
+            s.type  = 'Laplacian';
+            s.mesh  = obj.mesh;
+            s.test  = obj.velocityFun;
+            s.trial = obj.velocityFun;
+            LHS     = LHSIntegrator.create(s);
+            lhs     = n*LHS.compute();
+            lhs     = obj.symGradient(lhs);
+        end
+
+        function Kvs = computeVVA2Mat(obj)
+            s.type = 'StiffnessMatrixWithFunction';
+            s.mesh       = obj.mesh;
+            s.trial      = obj.velocityFun;
+            s.test       = obj.velocityFun;
+            s.function   = obj.velocityField;
+            s.function.setFValues(s.function.fValues .^2);
+            LHS = LHSIntegrator.create(s);
+            Kvs = LHS.compute();
+        end
+
+        function K = computeAVPMat(obj)
+            s.type       = 'StiffnessMatrixWithFunction';
+            s.mesh       = obj.mesh;
+            s.trial      = obj.pressureFun;
+            s.test       = obj.velocityFun;
+            s.function   = obj.velocityField;
+            LHS = LHSIntegrator.create(s);
+            K = LHS.compute();
+        end
+
+        function K = computePPMat(obj)
+            s.type       = 'StiffnessMatrix';
+            s.mesh       = obj.mesh;
+            s.trial      = obj.pressureFun;
+            s.test       = obj.pressureFun;
+            LHS = LHSIntegrator.create(s);
+            K = LHS.compute();
+        end
+
+        function A = symGradient(obj, B)
+            A = 1/2 * (B+B');
+        end
+
+        function M = computeMassMatrix(obj)
+            s.type  = 'MassMatrix';
+            s.mesh  = obj.mesh;
+            s.test  = obj.velocityFun;
+            s.trial = obj.velocityFun;
+            s.quadratureOrder = 3;
+            LHS = LHSIntegrator.create(s);
+            m = LHS.compute();
+
+            dtime = obj.dt;
+            M = m/dtime;
+        end
+
+        function KP = computePressureMatrix(obj)
+            s.type  = 'StiffnessMatrix';
+            s.mesh  = obj.mesh;
+            s.test  = obj.pressureFun;
+            s.trial = obj.pressureFun;
+            LHS = LHSIntegrator.create(s);
+            KP  = LHS.compute();
+
+        end
+
+        function LHS = addCMToLHS(obj,C)
+            LHS  = obj.LHSS;
+            nVel = size(C, 1);
+            LHS(1:nVel, 1:nVel) = LHS(1:nVel, 1:nVel) + C;
+        end
+
+        function LHS = addTermsToLHS(obj, C, tauS, Kvva2, Kavp, tauP, Kpva, Kpp, tauL, Kdvdv)
+            LHS  = obj.LHSS;
+            nVel = size(C, 1);
+
+            tauP = tauP(:);
+            tauS = tauS(:);
+            tauL = tauL(:);
+
+            Kvva2 = sparse(Kvva2);
+            KvS   = Kvva2 * tauS;
+
+            Kavp  = sparse(Kavp);
+            KpS   = Kavp * tauS;
+
+            Kpva  = sparse(Kpva);
+            KvP   = Kpva * tauP;
+
+            Kpp   = sparse(Kpp);
+            KpP   = Kpp * tauP;
+
+            Kdvdv = sparse(Kdvdv);
+            KvL   = Kdvdv * tauL;
+
+            LHS(1:nVel, 1:nVel)             = LHS(1:nVel, 1:nVel) + C + KvS + KvL; %+ KvL
+            LHS(1:nVel, nVel + 1:end)       = LHS(1:nVel, nVel + 1:end) + KpS;
+            LHS(nVel + 1:end, 1:nVel)       = LHS(nVel + 1:end, 1:nVel) + KvP;
+            LHS(nVel + 1:end, nVel + 1:end) = LHS(nVel + 1:end, nVel + 1:end) + KpP;
+        end
+
+        function tauS1 = computeTauS1(obj,CE,KE)
+            normCE = norm(CE,"fro");
+            normKE = norm(KE,"fro");
+            tauS1  = normCE / normKE;
+        end
+
+        function tauS3 = computeTauS3(obj, tauS1, a)
+            u   = norm(a,"fro");
+            tauS3 = tauS1 ^2 * u^2 / obj.nu;
+        end
+
+        function tau = computeTau(obj, tauS1,tauS3)
+            tau = (1/(tauS1^obj.residual) + 1/(tauS3^obj.residual)) ^(-1/obj.residual);
+        end
+
+        function tauP3 = computeTauP3(obj, tauP1, a, tauS1)
+            u   = norm(a,"fro");
+            tauP3 = tauP1 * u^2 / obj.nu * tauS1;
+        end
+
+    end
+
+end
\ No newline at end of file
diff --git a/src/Integrators/LHS/LHSIntegratorStokes.m b/src/Integrators/LHS/LHSIntegratorStokes.m
index f968670f27..ae78e6fe22 100644
--- a/src/Integrators/LHS/LHSIntegratorStokes.m
+++ b/src/Integrators/LHS/LHSIntegratorStokes.m
@@ -9,7 +9,7 @@
         mesh
         velocityFun
         pressureFun
-        material
+        nu
     end
 
     methods (Access = public)
@@ -32,7 +32,7 @@
         function init(obj, cParams)
             obj.dt          = cParams.dt;
             obj.mesh        = cParams.mesh;
-            obj.material    = cParams.material;
+            obj.nu          = cParams.nu;
             obj.pressureFun = cParams.pressureFun;
             obj.velocityFun = cParams.velocityFun;
         end
@@ -63,14 +63,14 @@ function init(obj, cParams)
         end
 
         function lhs = computeVelocityLaplacian(obj)
+            n       = obj.nu;
             s.type  = 'Laplacian';
             s.mesh  = obj.mesh;
             s.test  = obj.velocityFun;
             s.trial = obj.velocityFun;
-            s.material = obj.material;
-            LHS = LHSIntegrator.create(s);
-            lhs = LHS.compute();
-            lhs = obj.symGradient(lhs);
+            LHS     = LHSIntegrator.create(s);
+            lhs     = n*LHS.compute();
+            lhs     = obj.symGradient(lhs);
         end
 
         function M = computeMassMatrix(obj)
diff --git a/src/Integrators/RHS/RHSIntegratorFactory.m b/src/Integrators/RHS/RHSIntegratorFactory.m
index d1b0474274..07472b22da 100644
--- a/src/Integrators/RHS/RHSIntegratorFactory.m
+++ b/src/Integrators/RHS/RHSIntegratorFactory.m
@@ -31,6 +31,8 @@
                     obj = RHSIntegratorElasticMicro(cParams);
                 case 'Stokes'
                     obj = RHSIntegratorStokes(cParams);
+                case 'NavierStokes'
+                    obj = RHSIntegratorStokes(cParams);
                 case 'Unfitted'
                     obj = RHSIntegratorUnfitted(cParams);
             end
diff --git a/src/Integrators/RHS/RHSIntegratorStokes.m b/src/Integrators/RHS/RHSIntegratorStokes.m
index 5a81c09cad..9ef8892a53 100644
--- a/src/Integrators/RHS/RHSIntegratorStokes.m
+++ b/src/Integrators/RHS/RHSIntegratorStokes.m
@@ -38,7 +38,7 @@ function init(obj,cParams)
             a.mesh = obj.mesh;
             a.quadType = 3;
             rhsI       = RHSIntegrator.create(a);
-            test = LagrangianFunction.create(obj.mesh, 2, 'P2');
+            test = LagrangianFunction.create(obj.mesh, 2, obj.velocityFun.order);
             Fext = rhsI.compute(obj.forcesFormula,test);
         end
 
diff --git a/src/Materials/MaterialFactory.m b/src/Materials/MaterialFactory.m
index 2ddc905ce9..5aa471484d 100755
--- a/src/Materials/MaterialFactory.m
+++ b/src/Materials/MaterialFactory.m
@@ -18,9 +18,6 @@
                     
                 case 'DensityBased'
                     material = DensityBasedMaterial(cParams);
-                
-                case 'STOKES'
-                    material = MaterialStokes(cParams);
                     
                 case 'PhaseField'
                     switch cParams.PFtype
diff --git a/src/Materials/MaterialStokes.m b/src/Materials/MaterialStokes.m
deleted file mode 100644
index 3bee101527..0000000000
--- a/src/Materials/MaterialStokes.m
+++ /dev/null
@@ -1,24 +0,0 @@
-classdef MaterialStokes < Material
-    
-    properties (Access = public)
-        mu
-        nElem
-    end
-    
-    methods (Access = public) 
-        
-        function obj = MaterialStokes(cParams)
-            obj.nElem = cParams.nelem;
-        end
-
-        function compute(obj)
-            m = zeros(4,4,obj.nElem);
-            m(1,1,:) = 1;
-            m(2,2,:) = 1;
-            m(3,3,:) = 1;
-            m(4,4,:) = 1;
-            obj.mu = m;
-        end
-        
-    end
-end
\ No newline at end of file
diff --git a/src/NeuralNetwork/Data.m b/src/NeuralNetwork/Data.m
index 289da2cc31..50b6f5bf3a 100644
--- a/src/NeuralNetwork/Data.m
+++ b/src/NeuralNetwork/Data.m
@@ -20,6 +20,7 @@
         testRatio
         xFeatures
         yFeatures
+        k
     end
 
     methods (Access = public)
@@ -27,7 +28,7 @@
         function obj = Data(cParams)            
             obj.init(cParams)
             obj.loadData();
-            %obj.buildModel();
+            obj.buildModel();
             obj.splitdata()
             obj.nLabels   = size(obj.Ytrain,2);                        
             obj.nFeatures = size(obj.Xtrain,2);
@@ -84,14 +85,12 @@ function init(obj,cParams)
             obj.polynomialOrder = cParams.polynomialOrder;
             obj.xFeatures       = cParams.xFeatures;
             obj.yFeatures       = cParams.yFeatures;
+            obj.k               = cParams.k;
         end
 
         function loadData(obj)
-            %f = fullfile('../Datasets/',obj.fileName);
-            f = fullfile(obj.fileName);
 
-            % Change: use readmatrix to skip header
-            obj.data = readmatrix(f);
+            obj.data = load(obj.fileName).data;
 
             % Change: incorporate features to use in cParams vs propmpting
             % user though terminal
@@ -105,17 +104,19 @@ function loadData(obj)
         
 
         function Xful = buildModel(obj)
-            x  = obj.X;
-            d  = obj.polynomialOrder;
-            x1 = x(:,1);
-            x2 = x(:,2);
-            cont = 1;
-            for g = 1:d
-                for a = 0:g
-                    Xful(:,cont) = x2.^(a).*x1.^(g-a);
-                    cont = cont+1;
+            x    = obj.X;
+            Xful = x;
+            d    = obj.polynomialOrder;
+
+            if d > 1
+                
+                for i = 2:d
+                    tempX = x.^i;
+                    Xful = cat(2,Xful,tempX);
                 end
+            
             end
+
             obj.X = Xful;
         end
         
@@ -147,14 +148,34 @@ function loadData(obj)
         function splitdata(obj)
             nD = size(obj.data,1);
             TP = obj.testRatio;
-            r = randperm(nD);
             ntest = round(TP/100*nD);
-            ntrain = nD - ntest;
-            obj.Xtrain = obj.X(r(1:ntrain),:);
-            obj.Xtest  = obj.X(r((ntrain + 1):end),:);
-            obj.Ytrain = obj.Y(r(1:ntrain),:);
-            obj.Ytest  = obj.Y(r((ntrain + 1):end),:);
+            TestStart = 1 + ntest * (obj.k - 1.0);
+            TestEnd   = min(ntest * obj.k,nD); 
+            
+            testIdx = TestStart:TestEnd;
+            allIdx  = 1:nD;
+            trainIdx = setdiff(allIdx, testIdx);
+            obj.Xtrain = obj.X(trainIdx, :);
+            obj.Ytrain = obj.Y(trainIdx, :);
+            obj.Xtest  = obj.X(testIdx, :);
+            obj.Ytest  = obj.Y(testIdx, :);
             obj.Ntest = ntest;
         end
     end
+
+    methods (Access = public, Static)
+
+        function [NewData] = preProcessDataset(data)
+
+            nD = size(data,1);
+            r  = randperm(nD);
+            NewData = data(r(1:nD),:);
+
+            maxValue    = max(NewData(:,end));
+            minValue    = min(NewData(:,end));
+            NewData(:,end)  = (NewData(:,end) - minValue) / (maxValue - minValue);
+
+        end
+
+    end
 end
\ No newline at end of file
diff --git a/src/NeuralNetwork/SGD.m b/src/NeuralNetwork/SGD.m
index fa6d872457..95c72cc5c6 100644
--- a/src/NeuralNetwork/SGD.m
+++ b/src/NeuralNetwork/SGD.m
@@ -26,7 +26,7 @@
             obj.timeStop    = Inf([1,1]);
             obj.fvStop      = 1e-4;
             obj.nPlot       = 1;
-            obj.MaxEpochs   = s.maxEpochs;
+            obj.MaxEpochs   = s.maxEpochs; % 0.5e5
             obj.earlyStop   = obj.MaxEpochs;
             obj.svepoch     = 0;
             obj.lSearchType = 'static';
diff --git a/src/NeuralNetwork/Sh_Func_L2norm.m b/src/NeuralNetwork/Sh_Func_L2norm.m
index 2fae7cd4f2..4f85097306 100644
--- a/src/NeuralNetwork/Sh_Func_L2norm.m
+++ b/src/NeuralNetwork/Sh_Func_L2norm.m
@@ -1,7 +1,7 @@
 classdef Sh_Func_L2norm < handle
     
     properties (Access = private)
-       designVariable  
+       designVariable
     end
     
     methods (Access = public)
@@ -26,12 +26,12 @@
     methods (Access = private)
         
         function init(obj,cParams)
-            obj.designVariable = cParams.designVariable;
+            obj.designVariable  = cParams.designVariable;
         end
 
        function j = computeCost(obj)
            theta = obj.designVariable.thetavec;
-           j = 0.5*(theta)*theta';
+           j     =  0.5*(theta)*theta';
        end
 
        function dj = computeGradient(obj)
diff --git a/src/Problems/Projectors/Projector.m b/src/Problems/Projectors/Projector.m
index e5597685b4..5b9b3337d4 100644
--- a/src/Problems/Projectors/Projector.m
+++ b/src/Problems/Projectors/Projector.m
@@ -18,7 +18,7 @@
                 case 'ConstantFunction'
                     ord = 0;
                 case 'AnalyticalFunction'
-                    ord = 2;
+                    ord = 3;
                 case 'FEFunction'
                     ord = 2; % needed to project P1 to P1D             
                 otherwise
diff --git a/src/Problems/Projectors/ProjectorToLagrangian.m b/src/Problems/Projectors/ProjectorToLagrangian.m
index ad4636a95f..d6e1329a37 100644
--- a/src/Problems/Projectors/ProjectorToLagrangian.m
+++ b/src/Problems/Projectors/ProjectorToLagrangian.m
@@ -49,6 +49,7 @@
                     s.type  = 'MassMatrix';
                     lhs = LHSIntegrator.create(s);
                     LHS = lhs.compute();
+                    LHS = decomposition(LHS);
             end
         end
 
diff --git a/src/Problems/Stokes/Utilities/FittedNaca.m b/src/Problems/Stokes/Utilities/FittedNaca.m
new file mode 100644
index 0000000000..a63fffa118
--- /dev/null
+++ b/src/Problems/Stokes/Utilities/FittedNaca.m
@@ -0,0 +1,171 @@
+classdef FittedNaca < handle
+
+    properties (Access = private)
+        filename
+        mesh
+        nacaNodes
+        dY
+        young
+        poisson
+        material
+        stateProblem
+        mNew
+    end
+
+    methods (Access = public)
+
+        function obj = FittedNaca(file,mRef,pRef,tRef,m,p,t)
+            obj.init(file);
+            obj.createMesh();
+            obj.readNacaNodes();
+            obj.computeUpdatedNaca(mRef,pRef,tRef,m,p,t);
+            obj.computeElasticProperties();
+            obj.createMaterial();
+            obj.solveElasticProblem();
+            obj.createNewMesh();
+        end
+
+    end
+
+    methods (Access = private)
+
+        function init(obj,file)
+            obj.filename = file;
+        end
+
+        function createMesh(obj)
+            a.fileName = obj.filename;
+            s = FemDataContainer(a);
+            obj.mesh = s.mesh;
+        end
+
+        function readNacaNodes(obj)
+            a.fileName = obj.filename;
+            s = FemDataContainer(a);
+            obj.nacaNodes = unique(s.bc.dirichlet(:,1));
+        end
+
+        function computeUpdatedNaca(obj,mRef,pRef,tRef,m,p,t) % 0.02, 0.4, 0.12, 0.01, 0.2, 0.05
+            isUP      = obj.compueIsUp(mRef,pRef,tRef);
+            xNaca     = obj.mesh.coord(obj.nacaNodes,1);
+            yNaca     = obj.mesh.coord(obj.nacaNodes,2);
+            [yu,yl,~] = obj.computeNacaFunction(m,p,t,xNaca);
+
+            incY(isUP)  = yu(isUP) - yNaca(isUP);
+            incY(~isUP) = yl(~isUP) - yNaca(~isUP);
+
+            obj.dY = incY;
+        end
+
+        function computeElasticProperties(obj)
+            E  = 1;
+            nu = 1/3;
+            obj.young   = ConstantFunction.create(E,obj.mesh);
+            obj.poisson = ConstantFunction.create(nu,obj.mesh);
+        end
+
+        function createMaterial(obj)
+            s.type    = 'ISOTROPIC';
+            s.ptype   = 'ELASTIC';
+            s.ndim    = obj.mesh.ndim;
+            s.young   = obj.young;
+            s.poisson = obj.poisson;
+            tensor    = Material.create(s);
+            obj.material = tensor;
+        end
+
+        function solveElasticProblem(obj)
+            s.mesh = obj.mesh;
+            s.scale = 'MACRO';
+            s.material = obj.material;
+            s.dim = '2D';
+            s.boundaryConditions = obj.createBoundaryConditions();
+            s.solverType = 'REDUCED';
+            s.solverMode = 'DISP';
+            s.solverCase = 'DIRECT';
+            fem = ElasticProblem(s);
+            fem.solve();
+            obj.stateProblem = fem;
+        end
+
+        function isUP = compueIsUp(obj,m,p,t)              
+            xNaca = obj.mesh.coord(obj.nacaNodes,1);
+            yNaca = obj.mesh.coord(obj.nacaNodes,2);                        
+            [~,~,yc] = obj.computeNacaFunction(m,p,t,xNaca);
+            isUP = yNaca > yc;
+        end
+
+        function bc = createBoundaryConditions(obj)
+            dYCond      = obj.nacaNodes;
+            dYCond(:,2) = 2;
+            dYCond(:,3) = obj.dY;
+            sDir        = obj.computeCondition(dYCond);
+
+
+            xMin       = min(obj.mesh.coord(:,1));
+            yMin       = min(obj.mesh.coord(:,2));
+            xMax       = max(obj.mesh.coord(:,1));
+            yMax       = max(obj.mesh.coord(:,2));
+            isBoundary = @(coor)  coor(:,1)==xMin | coor(:,2)==yMin | coor(:,1)==xMax | coor(:,2)==yMax;
+            sDir{end+1}.domain    = @(coor) isBoundary(coor);
+            sDir{end}.direction = [1,2];
+            sDir{end}.value     = 0;
+
+            dirichletFun = [];
+            for i = 1:numel(sDir)
+                dir = DirichletCondition(obj.mesh, sDir{i});
+                dirichletFun = [dirichletFun, dir];
+            end
+            s.dirichletFun = dirichletFun;
+
+            s.pointloadFun = [];
+            s.periodicFun  = [];
+            s.mesh = obj.mesh;
+            bc = BoundaryConditions(s);
+        end
+
+        function createNewMesh(obj)
+            u = obj.stateProblem.uFun;
+
+            s.coord  = obj.mesh.coord + u.fValues;
+            s.connec = obj.mesh.connec;
+            obj.mNew = Mesh.create(s);
+        end
+
+    end
+
+    methods (Static, Access=private)
+        function [yu,yl,yc] = computeNacaFunction(m,p,t,xNaca)
+            yc   = (xNaca>=0 & xNaca<=p).*(m./p^2.*(2*p*xNaca-xNaca.^2))+...
+                (xNaca>p & xNaca<=1).*(m./(1-p)^2.*((1-2*p)+2*p*xNaca-xNaca.^2));
+            yt   = (xNaca>=0 & xNaca<=1).*(5*t*(0.2969*sqrt(xNaca)-0.1260*xNaca-0.3516*xNaca.^2+0.2843*xNaca.^3-0.1036*xNaca.^4));
+            dydx = (xNaca>=0 & xNaca<=p).*(2*m/p^2.*(p-xNaca))+...
+                (xNaca>p & xNaca<=1).*(2*m/(1-p)^2.*(p-xNaca));
+
+            theta = atan(dydx);
+            yu    = yc + yt.*cos(theta);
+            yl    = yc - yt.*cos(theta);
+
+        end
+
+        function sCond = computeCondition(conditions)
+            nodes = @(coor) 1:size(coor,1);
+            dirs  = unique(conditions(:,2));
+            j     = 0;
+            for k = 1:length(dirs)
+                rowsDirk = ismember(conditions(:,2),dirs(k));
+                u        = unique(conditions(rowsDirk,3));
+                for i = 1:length(u)
+                    rows   = conditions(:,3)==u(i) & rowsDirk;
+                    isCond = @(coor) ismember(nodes(coor),conditions(rows,1));
+                    j      = j+1;
+                    sCond{j}.domain    = @(coor) isCond(coor);
+                    sCond{j}.direction = dirs(k);
+                    sCond{j}.value     = u(i);
+                end
+            end
+        end
+
+    end
+
+end
\ No newline at end of file
diff --git a/src/Problems/Stokes/Utilities/Naca.gid/Naca.cnd b/src/Problems/Stokes/Utilities/Naca.gid/Naca.cnd
new file mode 100644
index 0000000000..d1bf07a49e
--- /dev/null
+++ b/src/Problems/Stokes/Utilities/Naca.gid/Naca.cnd
@@ -0,0 +1,456 @@
+NUMBER: 1 CONDITION: Point_Force
+CONDTYPE: over points
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load that will be applied to selected points}
+QUESTION: Fx
+VALUE: 0
+QUESTION: Fy
+VALUE: 0
+QUESTION: Fz
+VALUE: 0
+END CONDITION
+NUMBER: 2 CONDITION: x_direction_point_force
+CONDTYPE: over points
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load in x direction that will be applied to selected points}
+QUESTION: Fx
+VALUE: 0
+END CONDITION
+NUMBER: 3 CONDITION: y_direction_point_force
+CONDTYPE: over points
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load in y direction that will be applied to selected points}
+QUESTION: Fy
+VALUE: 0
+END CONDITION
+NUMBER: 4 CONDITION: z_direction_point_force
+CONDTYPE: over points
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load in z direction that will be applied to selected points}
+QUESTION: Fz
+VALUE: 0
+END CONDITION
+NUMBER: 5 CONDITION: Point_AdjointLoad
+CONDTYPE: over points
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load that will be applied to selected points}
+QUESTION: Fx
+VALUE: 0
+QUESTION: Fy
+VALUE: 0
+QUESTION: Fz
+VALUE: 0
+END CONDITION
+NUMBER: 6 CONDITION: Point_Constraint
+CONDTYPE: over points
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the constraints that will be applied to selected points}
+QUESTION: Ux
+VALUE: 0
+QUESTION: Uy
+VALUE: 0
+QUESTION: Uz
+VALUE: 0
+END CONDITION
+NUMBER: 7 CONDITION: x_direction_point_constraint
+CONDTYPE: over points
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the constraint in x direction that will be applied to selected points}
+QUESTION: Ux
+VALUE: 0
+END CONDITION
+NUMBER: 8 CONDITION: y_direction_point_constraint
+CONDTYPE: over points
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the constraints in y direction that will be applied to selected points}
+QUESTION: Uy
+VALUE: 0
+END CONDITION
+NUMBER: 9 CONDITION: z_direction_point_constraint
+CONDTYPE: over points
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the constraints in z direction that will be applied to selected points}
+QUESTION: Uz
+VALUE: 0
+END CONDITION
+NUMBER: 10 CONDITION: Line_Force
+CONDTYPE: over lines
+HELP: {Here you can define the Pressure that will be applied to selected lines}
+QUESTION: PressureX
+VALUE: 0
+QUESTION: PressureY
+VALUE: 0
+QUESTION: PressureZ
+VALUE: 0
+END CONDITION
+NUMBER: 11 CONDITION: x_direction_Line_Force
+CONDTYPE: over lines
+HELP: {Here you can define the Pressure in x direction that will be applied to selected lines}
+QUESTION: PressureX
+VALUE: 0
+END CONDITION
+NUMBER: 12 CONDITION: y_direction_Line_Force
+CONDTYPE: over lines
+HELP: {Here you can define the Pressure in y direction that will be applied to selected lines}
+QUESTION: PressureY
+VALUE: 0
+END CONDITION
+NUMBER: 13 CONDITION: z_direction_Line_Force
+CONDTYPE: over lines
+HELP: {Here you can define the Pressure in z direction that will be applied to selected lines}
+QUESTION: PressureZ
+VALUE: 0
+END CONDITION
+NUMBER: 14 CONDITION: Line_Load
+CONDTYPE: over lines
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load that will be applied to selected lines}
+QUESTION: Fx
+VALUE: 0
+QUESTION: Fy
+VALUE: 0
+QUESTION: Fz
+VALUE: 0
+END CONDITION
+NUMBER: 15 CONDITION: x_direction_Line_Load
+CONDTYPE: over lines
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load in x direction that will be applied to selected lines}
+QUESTION: Fx
+VALUE: 0
+END CONDITION
+NUMBER: 16 CONDITION: y_direction_Line_Load
+CONDTYPE: over lines
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load in y direction that will be applied to selected lines}
+QUESTION: Fy
+VALUE: 0
+END CONDITION
+NUMBER: 17 CONDITION: z_direction_Line_Load
+CONDTYPE: over lines
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load in z direction that will be applied to selected lines}
+QUESTION: Fz
+VALUE: 0
+END CONDITION
+NUMBER: 18 CONDITION: Line_AdjointLoad
+CONDTYPE: over lines
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load that will be applied to selected lines}
+QUESTION: Fx
+VALUE: 0
+QUESTION: Fy
+VALUE: 0
+QUESTION: Fz
+VALUE: 0
+END CONDITION
+NUMBER: 19 CONDITION: Line_Load_function
+CONDTYPE: over lines
+CONDMESHTYPE: over nodes
+HELP: {Here you can define a function/expresion which will be evaluated by the *Operation command in the bas file. \nUse \$x, \$y, \$z for the x, y and z coordinates of the node. For a 2D case, use online \$x and \$y}
+QUESTION: Fx
+VALUE: 0.0#WIDTH#(64)
+QUESTION: Fy
+VALUE: 0.0#WIDTH#(64)
+QUESTION: Fz
+VALUE: 0.0#WIDTH#(64)
+END CONDITION
+NUMBER: 20 CONDITION: Line_Constraint
+CONDTYPE: over lines
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the constraints that will be applied to selected lines}
+QUESTION: Ux
+VALUE: 0
+QUESTION: Uy
+VALUE: 0
+QUESTION: Uz
+VALUE: 0
+END CONDITION
+NUMBER: 21 CONDITION: x_direction_Line_Constraint
+CONDTYPE: over lines
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the constraints in x direction that will be applied to selected lines}
+QUESTION: Ux
+VALUE: 0
+END CONDITION
+NUMBER: 22 CONDITION: y_direction_Line_Constraint
+CONDTYPE: over lines
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the constraints in y direction that will be applied to selected lines}
+QUESTION: Uy
+VALUE: 0
+END CONDITION
+NUMBER: 23 CONDITION: z_direction_Line_Constraint
+CONDTYPE: over lines
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the constraints in z direction that will be applied to selected lines}
+QUESTION: Uz
+VALUE: 0
+END CONDITION
+NUMBER: 24 CONDITION: Line_Constraint_function
+CONDTYPE: over lines
+CONDMESHTYPE: over nodes
+HELP: {Here you can define a function/expresion which will be evaluated by the *Operation command in the bas file. \nUse \$x, \$y, \$z for the x, y and z coordinates of the node. For a 2D case, use online \$x and \$y}
+QUESTION: Ux
+VALUE: 0.0#WIDTH#(64)
+QUESTION: Uy
+VALUE: 0.0#WIDTH#(64)
+QUESTION: Uz
+VALUE: 0.0#WIDTH#(64)
+END CONDITION
+NUMBER: 25 CONDITION: Line_Border_elements
+CONDTYPE: over lines
+CONDMESHTYPE: over face elements
+HELP: {Here you can define the boundary lines to detect the elements that are included in the boundary}
+QUESTION: Border
+VALUE: 0
+END CONDITION
+NUMBER: 26 CONDITION: Line_Border_nodes
+CONDTYPE: over lines
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the boundary lines to detect the nodes that are included in the boundary}
+QUESTION: Border
+VALUE: 0
+END CONDITION
+NUMBER: 27 CONDITION: Surface_Force
+CONDTYPE: over surfaces
+CONDMESHTYPE: over face elements
+HELP: {Here you can define the Pressure that will be applied to selected surfaces}
+QUESTION: PressureX
+VALUE: 0
+QUESTION: PressureY
+VALUE: 0
+QUESTION: PressureZ
+VALUE: 0
+END CONDITION
+NUMBER: 28 CONDITION: x_direction_Surface_Force
+CONDTYPE: over surfaces
+CONDMESHTYPE: over face elements
+HELP: {Here you can define the Pressure in x direction that will be applied to selected surfaces}
+QUESTION: PressureX
+VALUE: 0
+END CONDITION
+NUMBER: 29 CONDITION: y_direction_Surface_Force
+CONDTYPE: over surfaces
+CONDMESHTYPE: over face elements
+HELP: {Here you can define the Pressure in y direction that will be applied to selected surfaces}
+QUESTION: PressureY
+VALUE: 0
+END CONDITION
+NUMBER: 30 CONDITION: z_direction_Surface_Force
+CONDTYPE: over surfaces
+CONDMESHTYPE: over face elements
+HELP: {Here you can define the Pressure in z direction that will be applied to selected surfaces}
+QUESTION: PressureZ
+VALUE: 0
+END CONDITION
+NUMBER: 31 CONDITION: Surface_Load
+CONDTYPE: over surfaces
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load that will be applied to selected surfaces}
+QUESTION: Fx
+VALUE: 0
+QUESTION: Fy
+VALUE: 0
+QUESTION: Fz
+VALUE: 0
+END CONDITION
+NUMBER: 32 CONDITION: x_direction_Surface_Load
+CONDTYPE: over surfaces
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load in x direction that will be applied to selected surfaces}
+QUESTION: Fx
+VALUE: 0
+END CONDITION
+NUMBER: 33 CONDITION: y_direction_Surface_Load
+CONDTYPE: over surfaces
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load in y direction that will be applied to selected surfaces}
+QUESTION: Fy
+VALUE: 0
+END CONDITION
+NUMBER: 34 CONDITION: z_direction_Surface_Load
+CONDTYPE: over surfaces
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the Load in z direction that will be applied to selected surfaces}
+QUESTION: Fz
+VALUE: 0
+END CONDITION
+NUMBER: 35 CONDITION: Surface_Load_function
+CONDTYPE: over surfaces
+CONDMESHTYPE: over nodes
+HELP: {Here you can define a function/expresion which will be evaluated by the *Operation command in the bas file. \nUse \$x, \$y, \$z for the x, y and z coordinates of the node. For a 2D case, use online \$x and \$y}
+QUESTION: Fx
+VALUE: 0.0#WIDTH#(64)
+QUESTION: Fy
+VALUE: 0.0#WIDTH#(64)
+QUESTION: Fz
+VALUE: 0.0#WIDTH#(64)
+END CONDITION
+NUMBER: 36 CONDITION: Surface_Constraint
+CONDTYPE: over surfaces
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the constraints that will be applied to selected surfaces}
+QUESTION: Ux
+VALUE: 0
+QUESTION: Uy
+VALUE: 0
+QUESTION: Uz
+VALUE: 0
+END CONDITION
+NUMBER: 37 CONDITION: x_direction_Surface_Constraint
+CONDTYPE: over surfaces
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the constraints in x direction that will be applied to selected surfaces}
+QUESTION: Ux
+VALUE: 0
+END CONDITION
+NUMBER: 38 CONDITION: y_direction_Surface_Constraint
+CONDTYPE: over surfaces
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the constraints in y direction that will be applied to selected surfaces}
+QUESTION: Uy
+VALUE: 0
+END CONDITION
+NUMBER: 39 CONDITION: z_direction_Surface_Constraint
+CONDTYPE: over surfaces
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the constraints in z direction that will be applied to selected surfaces}
+QUESTION: Uz
+VALUE: 0
+END CONDITION
+NUMBER: 40 CONDITION: Surface_Constraint_function
+CONDTYPE: over surfaces
+CONDMESHTYPE: over nodes
+HELP: {Here you can define a function/expresion which will be evaluated by the *Operation command in the bas file. \nUse \$x, \$y, \$z for the x, y and z coordinates of the node. For a 2D case, use online \$x and \$y}
+QUESTION: Ux
+VALUE: 0.0#WIDTH#(64)
+QUESTION: Uy
+VALUE: 0.0#WIDTH#(64)
+QUESTION: Uz
+VALUE: 0.0#WIDTH#(64)
+END CONDITION
+NUMBER: 41 CONDITION: Surface_Volumetric_force
+CONDTYPE: over surfaces
+HELP: {Here you can define the Volumetric force that will be applied to selected surfaces}
+QUESTION: Vol_forceX
+VALUE: 0
+QUESTION: Vol_forceY
+VALUE: 0
+QUESTION: Vol_forceZ
+VALUE: 0
+END CONDITION
+NUMBER: 42 CONDITION: Surface_x_direction_Volumetric_force
+CONDTYPE: over surfaces
+HELP: {Here you can define the Volumetric force in x direction that will be applied to selected surfaces}
+QUESTION: Vol_forceX
+VALUE: 0
+END CONDITION
+NUMBER: 43 CONDITION: Surface_y_direction_Volumetric_force
+CONDTYPE: over surfaces
+HELP: {Here you can define the Volumetric force in y direction that will be applied to selected surfaces}
+QUESTION: Vol_forceY
+VALUE: 0
+END CONDITION
+NUMBER: 44 CONDITION: Surface_z_direction_Volumetric_force
+CONDTYPE: over surfaces
+HELP: {Here you can define the Volumetric force in z direction that will be applied to selected surfaces}
+QUESTION: Vol_forceZ
+VALUE: 0
+END CONDITION
+NUMBER: 45 CONDITION: Boundary_elements
+CONDTYPE: over surfaces
+HELP: {Here you can define the surfaces whose elements can not be deleted}
+QUESTION: Boundary
+VALUE: 0
+END CONDITION
+NUMBER: 46 CONDITION: Initial_holes
+CONDTYPE: over surfaces
+HELP: {Here you can define the surfaces whose elements are voids initially}
+QUESTION: Holes
+VALUE: 0
+END CONDITION
+NUMBER: 47 CONDITION: Surface_Border_elements
+CONDTYPE: over surfaces
+CONDMESHTYPE: over face elements
+HELP: {Here you can define the boundary surfaces to detect the elements that are included in the boundary}
+QUESTION: Border
+VALUE: 0
+END CONDITION
+NUMBER: 48 CONDITION: Surface_Border_nodes
+CONDTYPE: over surfaces
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the boundary surfaces to detect the nodes that are included in the boundary}
+QUESTION: Border
+VALUE: 0
+END CONDITION
+NUMBER: 49 CONDITION: Volume_Volumetric_force
+CONDTYPE: over volumes
+CONDMESHTYPE: over body elements
+HELP: {Here you can define the Volumetric force that will be applied to selected volumes}
+QUESTION: Vol_forceX
+VALUE: 0
+QUESTION: Vol_forceY
+VALUE: 0
+QUESTION: Vol_forceZ
+VALUE: 0
+END CONDITION
+NUMBER: 50 CONDITION: Volume_x_direction_Volumetric_force
+CONDTYPE: over volumes
+CONDMESHTYPE: over body elements
+HELP: {Here you can define the Volumetric force in x direction that will be applied to selected volumes}
+QUESTION: Vol_forceX
+VALUE: 0
+END CONDITION
+NUMBER: 51 CONDITION: Volume_y_direction_Volumetric_force
+CONDTYPE: over volumes
+CONDMESHTYPE: over body elements
+HELP: {Here you can define the Volumetric force in y direction that will be applied to selected volumes}
+QUESTION: Vol_forceY
+VALUE: 0
+END CONDITION
+NUMBER: 52 CONDITION: Volume_z_direction_Volumetric_force
+CONDTYPE: over volumes
+CONDMESHTYPE: over body elements
+HELP: {Here you can define the Volumetric force in z direction that will be applied to selected volumes}
+QUESTION: Vol_forceZ
+VALUE: 0
+END CONDITION
+NUMBER: 53 CONDITION: Volume_Boundary_elements
+CONDTYPE: over volumes
+CONDMESHTYPE: over body elements
+HELP: {Here you can define the volumes whose elements can not be deleted}
+QUESTION: Boundary
+VALUE: 0
+END CONDITION
+NUMBER: 54 CONDITION: Volume_Initial_holes
+CONDTYPE: over volumes
+CONDMESHTYPE: over body elements
+HELP: {Here you can define the volumes whose elements are voids initially}
+QUESTION: Holes
+VALUE: 0
+END CONDITION
+NUMBER: 55 CONDITION: Micro_gauss
+CONDTYPE: over surfaces
+QUESTION: micro_gauss_point
+VALUE: 0
+END CONDITION
+NUMBER: 56 CONDITION: Line_Micro_Slave
+CONDTYPE: over lines
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the lines whose nodes are Master (1) or Slave (0)}
+QUESTION: Slave
+VALUE: 1
+END CONDITION
+NUMBER: 57 CONDITION: Surface_Micro_Slave
+CONDTYPE: over surfaces
+CONDMESHTYPE: over nodes
+HELP: {Here you can define the surfaces whose nodes are Master (1) or Slave (0)}
+QUESTION: Slave
+VALUE: 1
+END CONDITION
+NUMBER: 58 CONDITION: Group_value
+CONDTYPE: over surfaces
+QUESTION: Group
+VALUE: 0
+END CONDITION
diff --git a/src/Problems/Stokes/Utilities/Naca.gid/Naca.geo b/src/Problems/Stokes/Utilities/Naca.gid/Naca.geo
new file mode 100644
index 0000000000..9d9afa17a0
Binary files /dev/null and b/src/Problems/Stokes/Utilities/Naca.gid/Naca.geo differ
diff --git a/src/Problems/Stokes/Utilities/Naca.gid/Naca.lin b/src/Problems/Stokes/Utilities/Naca.gid/Naca.lin
new file mode 100644
index 0000000000..bd2b4aecad
Binary files /dev/null and b/src/Problems/Stokes/Utilities/Naca.gid/Naca.lin differ
diff --git a/src/Problems/Stokes/Utilities/Naca.gid/Naca.m b/src/Problems/Stokes/Utilities/Naca.gid/Naca.m
new file mode 100644
index 0000000000..c85332f44e
--- /dev/null
+++ b/src/Problems/Stokes/Utilities/Naca.gid/Naca.m
@@ -0,0 +1,54551 @@
+%==================================================================
+%                        General Data File
+% Title: Default_title
+% Units: SI
+% Dimensions: 2D
+% Type of problem: Plane_Stress
+% Type of Phisics: ELASTIC
+% Micro/Macro: MACRO
+%
+%==================================================================
+
+%% Data
+
+Data_prb = {
+'Default_title';
+'SI';
+'2D';
+'Plane_Stress';
+'ELASTIC';
+'MACRO';
+};
+
+%% Coordinates
+% Node                X                Y                Z
+
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+];
+
+%% Conectivities
+% Element        Node(1)                Node(2)                Node(3)                Material
+
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+];
+
+%% Variable Prescribed
+% Node            Dimension                Value
+
+lnodes = [
+9877 1 0 
+9877 2 0 
+9882 1 0 
+9882 2 0 
+10004 1 0 
+10004 2 0 
+10018 1 0 
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+11926 1 0 
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+];
+
+%% Force Prescribed
+% Node                Dimension                Value
+
+pointload_complete = [
+];
+
+pointload_adjoint = [
+];
+
+%% Volumetric Force
+% Element        Dim                Force_Dim
+
+Vol_force = [
+];
+
+%% Group Elements
+% Element        Group_num
+
+Group = [
+];
+
+%% Initial Holes
+% Elements that are considered holes initially
+% Element
+
+Initial_holes = [
+];
+
+%% Boundary Elements
+% Elements that can not be removed
+% Element
+
+Boundary_elements = [
+];
+
+%% Micro gauss post
+%
+% Element
+
+Micro_gauss_post = [
+];
+
+
+%% Micro Slave-Master
+% Nodes that are Slaves
+% Nodes             Value (1-Slave,0-Master)
+
+Micro_slave = [
+];
+
+%% Nodes solid
+% Nodes that must remain 
+% Nodes
+
+if ~isempty(pointload_complete)
+    nodesolid = unique(pointload_complete(:,1));
+end
+
+%% External border Elements
+% Detect the elements that define the edge of the domain
+% Element               Node(1)           Node(2)
+
+External_border_elements = [
+];
+
+%% External border Nodes
+% Detect the nodes that define the edge of the domain
+% Node
+
+External_border_nodes = [
+];
+
+%% Materials
+% Materials that have been used
+% Material_Num              Mat_density        Young_Modulus        Poisson
+
+Materials = [
+];
diff --git a/src/Problems/Stokes/Utilities/Naca.gid/Naca.mat b/src/Problems/Stokes/Utilities/Naca.gid/Naca.mat
new file mode 100644
index 0000000000..07a5905155
--- /dev/null
+++ b/src/Problems/Stokes/Utilities/Naca.gid/Naca.mat
@@ -0,0 +1,112 @@
+NUMBER: 1 MATERIAL: Unity
+QUESTION: Density
+VALUE: 1
+QUESTION: Young
+VALUE: 1
+QUESTION: Poisson
+VALUE: 0.3
+END MATERIAL
+NUMBER: 2 MATERIAL: Air
+QUESTION: Density
+VALUE: 1.01
+QUESTION: Young
+VALUE: 0.001
+QUESTION: Poisson
+VALUE: 0.00
+END MATERIAL
+NUMBER: 3 MATERIAL: Steel
+QUESTION: Density
+VALUE: 7850
+QUESTION: Young
+VALUE: 210e9
+QUESTION: Poisson
+VALUE: 0.30
+END MATERIAL
+NUMBER: 4 MATERIAL: Iron
+QUESTION: Density
+VALUE: 7800
+QUESTION: Young
+VALUE: 180e9
+QUESTION: Poisson
+VALUE: 0.23
+END MATERIAL
+NUMBER: 5 MATERIAL: Aluminium
+QUESTION: Density
+VALUE: 2650
+QUESTION: Young
+VALUE: 75e9
+QUESTION: Poisson
+VALUE: 0.32
+END MATERIAL
+NUMBER: 6 MATERIAL: Titanium
+QUESTION: Density
+VALUE: 4600
+QUESTION: Young
+VALUE: 105e9
+QUESTION: Poisson
+VALUE: 0.265
+END MATERIAL
+NUMBER: 7 MATERIAL: Magnesium
+QUESTION: Density
+VALUE: 1845
+QUESTION: Young
+VALUE: 44.5e9
+QUESTION: Poisson
+VALUE: 0.252
+END MATERIAL
+NUMBER: 8 MATERIAL: Concrete
+QUESTION: Density
+VALUE: 2350
+QUESTION: Young
+VALUE: 31.5e9
+QUESTION: Poisson
+VALUE: 0.15
+END MATERIAL
+NUMBER: 9 MATERIAL: Brick
+QUESTION: Density
+VALUE: 2000
+QUESTION: Young
+VALUE: 30e9
+QUESTION: Poisson
+VALUE: 0.30
+END MATERIAL
+NUMBER: 10 MATERIAL: Water
+QUESTION: Density
+VALUE: 997
+QUESTION: Young
+VALUE: 0.001
+QUESTION: Poisson
+VALUE: 0.30
+END MATERIAL
+NUMBER: 11 MATERIAL: Sand
+QUESTION: Density
+VALUE: 1370
+QUESTION: Young
+VALUE: 0.001
+QUESTION: Poisson
+VALUE: 0.325
+END MATERIAL
+NUMBER: 12 MATERIAL: CFRP
+QUESTION: Density
+VALUE: 1550
+QUESTION: Young
+VALUE: 109.5e9
+QUESTION: Poisson
+VALUE: 0.30
+END MATERIAL
+NUMBER: 13 MATERIAL: GFRP
+QUESTION: Density
+VALUE: 1850
+QUESTION: Young
+VALUE: 21.5e9
+QUESTION: Poisson
+VALUE: 0.29
+END MATERIAL
+NUMBER: 14 MATERIAL: Wood
+QUESTION: Density
+VALUE: 800
+QUESTION: Young
+VALUE: 13e9
+QUESTION: Poisson
+VALUE: 0.20
+END MATERIAL
diff --git a/src/Problems/Stokes/Utilities/Naca.gid/Naca.msh b/src/Problems/Stokes/Utilities/Naca.gid/Naca.msh
new file mode 100644
index 0000000000..b6a9a2a1d3
Binary files /dev/null and b/src/Problems/Stokes/Utilities/Naca.gid/Naca.msh differ
diff --git a/src/Problems/Stokes/Utilities/Naca.gid/Naca.png b/src/Problems/Stokes/Utilities/Naca.gid/Naca.png
new file mode 100644
index 0000000000..2fb0557de2
Binary files /dev/null and b/src/Problems/Stokes/Utilities/Naca.gid/Naca.png differ
diff --git a/src/Problems/Stokes/Utilities/Naca.gid/Naca.prb b/src/Problems/Stokes/Utilities/Naca.gid/Naca.prb
new file mode 100644
index 0000000000..e737800ebc
--- /dev/null
+++ b/src/Problems/Stokes/Utilities/Naca.gid/Naca.prb
@@ -0,0 +1,16 @@
+PROBLEM DATA
+QUESTION: Title
+VALUE: Default_title
+QUESTION: Unit_System:#CB#(SI,CGS,User)
+VALUE: SI
+QUESTION: DIMENSIONS:#CB#(1D,2D,3D)
+VALUE: 2D
+QUESTION: TYPE_OF_PROBLEM:#CB#(Plane_Stress,Plane_Strain)
+VALUE: Plane_Stress
+QUESTION: PHYSICAL_TYPE:#CB#(THERMAL,ELASTIC)
+VALUE: ELASTIC
+QUESTION: MACRO/MICRO:#CB#(MACRO,MICRO)
+VALUE: MACRO
+END PROBLEM DATA
+INTERVAL DATA
+END INTERVAL DATA
diff --git a/src/Problems/Stokes/Utilities/Naca.gid/Naca.tree b/src/Problems/Stokes/Utilities/Naca.gid/Naca.tree
new file mode 100644
index 0000000000..d384111098
--- /dev/null
+++ b/src/Problems/Stokes/Utilities/Naca.gid/Naca.tree
@@ -0,0 +1,9 @@
+<?xml version="1.0" encoding="utf-8"?>
+<gid>
+  <pre>
+    <groups_open>
+    </groups_open>
+    <layers_open>
+    </layers_open>
+  </pre>
+</gid>
diff --git a/src/Problems/Stokes/Utilities/Naca.gid/Naca.vv b/src/Problems/Stokes/Utilities/Naca.gid/Naca.vv
new file mode 100644
index 0000000000..597d08abfc
--- /dev/null
+++ b/src/Problems/Stokes/Utilities/Naca.gid/Naca.vv
@@ -0,0 +1,33 @@
+BeginZE
+   x -1.11339294910430908 2.66670322418212891
+   y 0.938933908939361572 -0.919367611408233643
+   z -16.9785137176513672 16.9785137176513672
+   e 5.37746095657348633
+   v 0 0 0
+   r 1
+   m 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
+   c 0.781988680362701416 0.012686803936958313 0
+   pd 0
+   pno 0
+   pfo 0
+   pf 4
+   pv 0
+   NowUse 1
+   DrawingType 0
+   LightVector 90 90 150 0
+   OGLShadow(UseShadows) 0
+   OGLShadow(RenderMode) RenderNice
+   OGLShadow(ShadowBias) -0.002
+   OGLShadow(AmbientShadows) 1
+   OGLShadow(UseFBO) 1
+   OGLShadow(FBOSize) 2048
+   OGLShadow(DimmedLightFactor) 0.02
+   OGLStereo(UseStereo) 0
+   OGLStereo(RelativeEyeDistance) 1
+   OGLStereo(FlipEyes) 0
+   OGLStereo(StereoMode) AnaglyphColors
+   OGLStereo(EyeDistance) 0.075
+   OGLStereo(LeftEyeDistance) 1 0 0 1
+   OGLStereo(RightEyeDistance) 0 1 1 1
+EndZE
+
diff --git a/src/UnfittedMesh/GeometricalFunction.m b/src/UnfittedMesh/GeometricalFunction.m
index 541afd82c3..fd715a88f5 100644
--- a/src/UnfittedMesh/GeometricalFunction.m
+++ b/src/UnfittedMesh/GeometricalFunction.m
@@ -42,7 +42,7 @@ function selectHandle(obj,cParams)
                     x0 = cParams.xCoorCenter;
                     y0 = cParams.yCoorCenter;
                     p  = cParams.pnorm;
-                    fH = @(x) (((abs(x1(x)-x0)).^p+(abs(x2(x)-y0)).^p).^(1/p))/l - 0.5;
+                    fH = @(x) ((abs(x1(x)-x0).^p+abs(x2(x)-y0).^p).^(1/p))/l - 0.5;
                     obj.fHandle = fH;
 
                 case 'SquareInclusion'
@@ -51,25 +51,13 @@ function selectHandle(obj,cParams)
                     obj.computeInclusion(s);
 
                 case 'Rectangle'
-                   % sx = (cParams.xSide)/2;
-                   % sy = (cParams.ySide)/2;
-                    % sx = (1-cParams.xSide)/2;
-                    % sy = (1-cParams.ySide)/2;    
-                    % sx = cos(2*pi*sx);
-                    % sy = cos(2*pi*sy);                      
-                    % x0 = cParams.xCoorCenter;
-                    % y0 = cParams.yCoorCenter;
-                    % fH = @(x) max((x1(x)-x0)./(sx),(x2(x)-y0)./(sy)) - 1;
-                    % obj.fHandle = fH;
-
                     sx = cParams.xSide;
                     sy = cParams.ySide;
                     x0 = cParams.xCoorCenter;
                     y0 = cParams.yCoorCenter;
-                    fH = @(x) max(abs(x1(x)-x0)./sx,abs(x2(x)-y0)./sy) - 0.5;
+                    fH = @(x) max(abs(x1(x)-x0)/sx,abs(x2(x)-y0)/sy) - 0.5;
                     obj.fHandle = fH;
 
-
                 case 'RectangleInclusion'
                     s      = cParams;
                     s.type = 'Rectangle';
@@ -81,25 +69,13 @@ function selectHandle(obj,cParams)
                     obj.computeInclusion(s);
 
                 case 'SmoothRectangle'
-                     % sx = (cParams.xSide)/2;
-                     % sy = (cParams.ySide)/2;
-                %   sx = (1-cParams.xSide)/2;
-                %   sy = (1-cParams.ySide)/2;    
-                %   sx = cos(2*pi*sx);
-                %   sy = cos(2*pi*sy);                      
-                    % x0 = cParams.xCoorCenter;
-                    % y0 = cParams.yCoorCenter;
-                    % p  = cParams.pnorm;
-                    % fH = @(x) (((x1(x)-x0)./(sx)).^p+((x2(x)-y0)./(sy)).^p).^(1/p) - 1;
-                    % obj.fHandle = fH;
-
                     sx = cParams.xSide;
                     sy = cParams.ySide;
                     x0 = cParams.xCoorCenter;
                     y0 = cParams.yCoorCenter;
                     p  = cParams.pnorm;
-                    fH = @(x) ((abs(x1(x)-x0)./sx).^p+(abs(x2(x)-y0)./sy).^p).^(1/p) - 0.5;
-                    obj.fHandle = fH;                    
+                    fH = @(x) ((abs(x1(x)-x0)/sx).^p+(abs(x2(x)-y0)/sy).^p).^(1/p) - 0.5;
+                    obj.fHandle = fH;
 
                 case 'RectangleRotated'
                     sx = cParams.xSide;
@@ -236,12 +212,17 @@ function selectHandle(obj,cParams)
                     obj.fHandle = fH;
 
                 case 'Vigdergauz'
-                    fH          = LevelSetVigdergauz(cParams);
-                    obj.fHandle = fH.getFunctionHandle();
+                    vig         = LevelSetVigdergauz(cParams);
+                    obj.fHandle = vig.getFunctionHandle();
 
                 case 'PeriodicAndOriented'
-                    fH          = LevelSetPeriodicAndOriented(cParams);
-                    obj.fHandle = fH.getFunctionHandle();
+                    perOr       = LevelSetPeriodicAndOriented(cParams);
+                    obj.fHandle = perOr.getFunctionHandle();
+
+                case 'Naca'
+                    fH = @(x) obj.createNacaHole(x1(x),x2(x),cParams);
+                    obj.fHandle = fH;
+
                 case 'Hexagon'
                     l  = cParams.radius;
                     n  = cParams.normal;
@@ -287,5 +268,43 @@ function computeInclusion(obj,s)
             d = (normVn/(l*(sqrt(3)/2)))-1;
         end
 
+        function fV = createNacaHole(x,y,s)
+            c   = s.chord;
+            p   = s.p;
+            m   = s.m;
+            t   = s.t;
+            AoA = deg2rad(s.AoA);
+        
+            x0      = s.xLE;
+            y0      = s.yLE/c;
+            offsetX = (x - x0)/c;
+            offsetY = y/c - y0;
+
+            xNaca    = offsetX.*cos(AoA) - offsetY.*sin(AoA);
+            yNaca    = offsetX.*sin(AoA) + offsetY.*cos(AoA);
+
+            if (m > 1e-6)
+               yc   = (xNaca>=0 & xNaca<=p).*(m./p^2.*(2*p*xNaca-xNaca.^2))+...
+                    (xNaca>p & xNaca<=1).*(m./(1-p)^2.*((1-2*p)+2*p*xNaca-xNaca.^2));
+               dydx = (xNaca>=0 & xNaca<=p).*(2*m/p^2.*(p-xNaca))+...
+                    (xNaca>p & xNaca<=1).*(2*m/(1-p)^2.*(p-xNaca));
+            else
+                yc   = 0;
+                dydx = 0;
+            end
+          
+            yt   = (xNaca>=0 & xNaca<=1).*(5*t*(0.2969*sqrt(xNaca)-0.1260*xNaca-0.3516*xNaca.^2+0.2843*xNaca.^3-0.1036*xNaca.^4));
+            
+            theta = atan(dydx);
+            yu    = yc + yt.*cos(theta);
+            yl    = yc - yt.*cos(theta);
+            
+            f(:,:,:,1)   = yl - yNaca;
+            f(:,:,:,2)   = yNaca - yu;
+            f(:,:,:,3)   = xNaca - 0.961; 
+            f(:,:,:,4)   = -xNaca;
+            
+            fV = -max(f,[],4);       
+        end    
     end
 end
\ No newline at end of file
diff --git a/src/UnfittedMesh/UnfittedMesh.m b/src/UnfittedMesh/UnfittedMesh.m
index ec7fe23bd7..bc82098360 100644
--- a/src/UnfittedMesh/UnfittedMesh.m
+++ b/src/UnfittedMesh/UnfittedMesh.m
@@ -99,7 +99,8 @@ function printNew(obj,filename)
             ls.print(filename, 'GiD');
         end
 
-        function m = createFullInnerMesh(obj, s)
+        function m = createFullInnerMesh(obj, type)
+            s.type         = type;
             s.unfittedMesh = obj;
             imc = FullInnerMeshCreator.create(s);
             m = imc.export();