Schéma volumes finis pour des opérateurs de diffusion fortement anisotropes sur des maillages non structurés

We introduce a finite volume method for highly anisotropic diffusion operators on unstructured meshes. The main idea is to calculate the gradient on each cell vertex using the cell-centered unknown and other unknowns calculated on the cell edges. These degrees of freedom are eliminated imposing flux continuity conditions. The resulting global matrix is symmetric and positive definite. We show the robustness and the precision of the method in comparison with analytical solutions and results obtained by other numerical schemes. To cite this article: C. Le Potier, C. R. Acad. Sci. Paris, Ser. I 340 (2005).