Argyris RefFE

[oriolcg]

Hi @Antoinemarteau , I've seen that you did a lot of work on the moment-based RefFEs lately. Would it be possible to add other elements for C1 continuity like Argyris: https://defelement.org/elements/argyris.html ? Would it require a lot of work?

Thanks!

[Antoinemarteau]

Hi Oriol, yeah actually I mostly touched Polynomials and documented ReferenceFEs, but @JordiManyer coded most of the new features.

Regarding C1 FEs, to my sparse understanding, they are not purely reference finite elements because the DoFs that are point-wise derivative based must be evaluated in the physical space. So they do not directly belong to the moment-based FE framework that was just implemented.

I can discuss with Santi in July if I may work on this, I might need this later, but I'm not sure.

[JordiManyer]

Hi @oriolcg the pupose of the refactor is that more complicated elements (like Argyris) become easier to implement. If you are interested in Argyris, I encourage you to maybe try and implement it. There are a couple of things missing to be able to implement absolutely everything, but you can probably get close.

[Antoinemarteau]

This paper seems to be a good one to start from, you should work on top of the moment-based-reffe branch and might:

• use the MomentBasedReferenceFE to implement the dof basis, that support evaluation of bof point-wise evaluation at vertices and integral normal moments on 2-facets (edges)
• overload Pushforward function from ReferenceFEs/Pullbacks.jl and get_cell_shapefuns and get_cell_dof_basis from FESpaces/Pullbacks.jl on the new element to add the necessary physical cell dependent transformations

[zjwegert]

Hi @oriolcg, did you make much progress with this? I'm interested in using(/maybe implementing) these types of elements as well