A Cell-Centered Scheme For Heterogeneous Anisotropic Diffusion Problems On General Meshes

Abstract: We present a new scheme for the discretization of heterogeneous anisotropic diffusion problems on general meshes. With light assumptions, we show that the algorithm can be written as a cell-centered scheme with a small stencil and that it is convergent for discontinuous tensors. The key point of the proof consists in showing both the strong and the weak consistency of the method. The efficiency of the scheme is demonstrated through numerical tests of the 5th International Symposium on Finite Volumes for Complex Appli- cations - FVCA 5. Moreover, the comparison with classical finite volume schemes emphasizes the precision of the method. We also show the good behaviour of the algorithm for nonconforming meshes.

Key words : Heterogeneous anisotropic diffusion, general grids, finite volumes, finite elements, cell-centered scheme.

Paper presented by : Professor Thierry Gallouët