Hello Everyone,
I would be interested in solving the biharmonic equation with Dirichlet and Neumann boundary conditions using a conforming finite element method, i.e., the finite dimensional spaces are always subspaces of the Sobolev space where solutions are sought.
According to Cahpter 6 of the monograph by Ciarlet(1978), such a discretisation can be performed using, for instance, the Hsieh-Clough-Tocher triangle (a.k.a. HCT).
I long searched for such an element, but I could not find it in the Fenics library.
Do you know how I could load the HCT element library onto my python script (if it is possible, of course)?
I do not think this is implemented in FEniCS (anyone correct me if Im wrong). However, you could have a look at the firedrake project, see for instance: https://arxiv.org/pdf/2002.02051.pdf
Firedrake supports Argyris element which is also conforming. See the paper and the linked Zenodo archive to get the codes used in it (specifically, the ones used to solve biharmonic equation)
Thank you very much for the replies. Indeed, Firedrake supports Argyris.
I also noticed here that the Argyris triangle is built-in, but is only “partially supported”.
Would you know if the Fenics council will be implementing these elements in the next release?