Comparison of finite element and finite box discretization for three-dimensional diffusion modeling using AMIGOS

The occurrence of unphysical negative concentrations in solutions to diffusion equations is a well known and severe problem. Especially in three dimensions finite element discretizations give qualitatively very poor results, while finite volume discretizations are much more stable. We investigate the cause of these instabilities and trace them back to constraints on the mesh. It turns out that in three dimensions conventional (i.e. Delaunay) meshes are only suitable for the finite box method, while Delaunay is an invalid constraint in the case of finite elements