Benchmark on anisotropic problems. A Galerkin Finite Element Solution.

Titre du congrès :5th International Symposium on Finite Volumes for Complex Applications Ville du congrès :Aussois Date du congrès :08/06/2008

We propose in this paper a contribution to the FVCA V benchmark on anisotropic diffusion problems using Galerkin finite element methods. This contribution addresses all the proposed cases the mesh of which is conforming, and those ones the mesh of which can be obtained by successive local refinement of a coarse conforming one. In this latter case, the CHARMS method is used to build the approximation space. Linear and quadratic elements are tested. Theoretical convergence orders are always recovered. Some undershoots or overshoots of the discrete solution beyond the maximum-principle-based theoretical bounds are observed; they quickly decrease when refining the mesh.