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

We introduce a new finite volume method for highly anisotropic diffusion operators on unstructured meshes. The main idea is to calculate the gradient using a nonlinear scheme. For parabolic problems, if the time step is small enough, the resulting global matrix is monotone without geometrical constraints on the mesh and restrictive conditions on the anisotropy ratio. We check the precision of the method in comparison with analytical solutions. The efficiency of the algorithm is demonstrated by comparing it with numerical schemes which do not satisfy a discrete maximum principle on the studied case. To cite this article: C. Le Potier, C. R. Acad. Sci. Paris, Ser. I 341 (2005).