A mixed finite volume scheme for anisotropic diffusion problems on any grid

J. Droniou (1) , Robert Eymard (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution and of its gradient. In the case of simplicial meshes, the approximate solution is shown to converge to the continuous ones as the size of the mesh tends to 0, and an error estimate is given. In the general case, we propose a slightly modified scheme for which we again prove the convergence, and give an error estimate. An easy implementation method is then proposed, and the efficiency of the scheme is shown on various types of grids.

Mots clés: Finite volume scheme; unstructured grids; irregular grids; anisotropic diffusion problems

Domaines: Analyse numérique [math.NA]

J. Droniou, Robert Eymard. A mixed finite volume scheme for anisotropic diffusion problems on any grid. Numerische Mathematik, 2006, 105, http://rd.springer.com/article/10.1007/s00211-006-0034-1. ⟨10.1007/s00211-006-0034-1⟩. ⟨hal-00005565v3⟩