We have an application that requires C_2 elements. I tried even a simpler C_1 element:
self.V = FunctionSpace(self.mesh, 'HER', 3)
(mesh is a 3D mesh) However, I get the following error:
This element family (Hermite) is not supported by FFC
Is there support for C_1 or even C_2 elements?
I also looked at the Argyris triangles, which are C_2 at the vertices, which is also sufficient for this application. However, is there a generalization to 3D tetrahedra, and are these supported?
It is not supported directly. I made a library that works around this limitation, to do isogeometric analysis (IGA) in FEniCS, although usage is slightly different from standard FE analysis:
If you have some other code that can evaluate the basis functions for a smooth basis on simplicial elements, it shouldn’t be too hard to wrap a subclass of AbstractExtractionGenerator around it and use this basis in tIGAr, but I have only implemented splines based on quad/hex elements so far (with an inefficient fallback option to break each quad/hex into simplices), e.g., B-splines, NURBS, and T-splines (although the latter requires an input file from a Rhino plugin that is no longer available).