Discretisation of heterogeneous and anisotropic diffusion problems on general non-conforming meshes. SUSHI: a scheme using stabilisation and hybrid interfaces

Robert Eymard (1) , Thierry Gallouët (2) , Raphaele Herbin (2)

1 LETEM - Laboratoire d'Etudes des Transferts d'Energie et de Matière
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

A discretisation scheme for heterogeneous anisotropic diffusion problems on general meshes is developed and studied. The unknowns of this scheme are the values at the centre of the control volumes and at some internal interfaces which may for instance be chosen at the diffusion tensor discontinuities. The scheme is therefore completely cell centred if no edge unknown is kept. It is shown to be accurate on several numerical examples. Mathematical convergence of the approximate solution to the continuous solution is obtained for general (possibly discontinuous) tensors, general (possibly non-conforming) meshes, and with no regularity assumption on the solution. An error estimate is then drawn under sufficient regularity assumptions on the solution.

Mots clés: Heterogeneous anisotropic diffusion; nonconforming grids; finite volume schemes

Domaines: Analyse numérique [math.NA]

Robert Eymard, Thierry Gallouët, Raphaele Herbin. Discretisation of heterogeneous and anisotropic diffusion problems on general non-conforming meshes. SUSHI: a scheme using stabilisation and hybrid interfaces. 2008. ⟨hal-00203269v4⟩