Reading group

Firedrake reading group

An informal reading group around many things finite element. Hosted online. Email Lawrence Mitchell if you'd like to participate.

Scheduled time: Mondays 17:00UTC. This calendar contains details.

Hosted via Zoom:

• Meeting ID: 928 2384 2685
• Passcode: 494089

Upcoming sessions

• 2021-02-15 MK leading Accurate Discretization Of Poroelasticity Without Darcy Stability -- Stokes-Biot Stability Revisited, Kent-Andre Mardal, Marie E. Rognes, Travis B. Thompson https://arxiv.org/pdf/2007.10012.pdf
• 2021-02-22 THG leading Multigrid preconditioners for the hybridized Discontinuous Galerkin discretisation of the shallow water equations, Jack D. Betteridge, Thomas H. Gibson, Ivan G. Graham, Eike H. Mueller https://arxiv.org/pdf/2004.09389.pdf

Possible papers

Please add your own, or claim one to present.

• Bonizzoni and Kanschat, H¹-conforming finite element cochain complexes and commuting quasi-interpolation operators on cartesian meshes (2020).

• Li, Zhang, and Zhang, A constrained transport divergence-free finite element method for Incompressible MHD equations (2020).

• Xu, The method of subspace corrections (2001).

• Hiptmair and Pechstein, Discrete regular decompositions of tetrahedral discrete 1-forms (2017). This paper introduces, in a rather didactic way, a lot of modern analysis tools for development and analysis of preconditioners for H(div) and H(curl) problems.

Past editions

2021-02-01 LM leading Space-time block preconditioning for incompressible flow, Danieli, Southworth, Wathen https://arxiv.org/abs/2101.07003

2020-12-14 DAH went over a proposal to properly add dual spaces in UFL, and the consequences thereof. Now available on the arxiv.

2020-12-07 CJC covered some of the (relatively new) developments in parallel in time stuff, going over the introduction to ParaDIAG from Martin Gander and friends.

2020-11-30 FW covered one paper on the new hotness of using neural nets for everything: Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar, Fourier Neural Operator for Parametric Partial Differential Equations (2020)

2020-11-23 FW covered the (now sadly bitrotted) automated adaptivity that used to be implemented in Dolfin, described in Marie E. Rognes and Anders Logg, Automated Goal-Oriented Error Control I: Stationary Variational Problems (2013).

2020-11-09 EM went through Mardal and Winther, Preconditioning discretizations of systems of partial differential equations (2011).

2020-10-26 & 2020-11-02 IP talked us through the construction and analysis of the Stokes-Darcy element introduced in Mardal, Tai, and Winther, A robust finite element method for Darcy-Stokes flow (2002). (Available in Firedrake as FunctionSpace(triangular_mesh, "MTW", 3)).

2020-10-12 & 2020-10-19. CJC talked us through the main points of Demkowicz and Gopalakrishnan, An overview of the discontinuous Petrov Galerkin method (2014).

Summer 2020. We read through Joachim Schöberl's thesis on parameter-robust multigrid methods. Some notes are collected.

Autumn/Winter 2019. We read Doug Arnold's book on Finite Element Exterior Calculus.