An asymptotic preserving scheme for strongly anisotropic elliptic problems

Pierre Degond (1) , Fabrice Deluzet (1) , Claudia Negulescu (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

In this article we introduce an asymptotic preserving scheme designed to compute the solution of a two dimensional elliptic equation presenting large anisotropies. We focus on an anisotropy aligned with one direction, the dominant part of the elliptic operator being supplemented with Neumann boundary conditions. A new scheme is introduced which allows an accurate resolution of this elliptic equation for an arbitrary anisotropy ratio.

Mots clés: Asymptotic Preserving scheme; Anisotropic elliptic equation; Numerics; Ill-conditioned problem; Singular Perturbation Model; Limit Model; Asymptotic Preserving scheme.

Domaines: Analyse numérique [math.NA]

Pierre Degond, Fabrice Deluzet, Claudia Negulescu. An asymptotic preserving scheme for strongly anisotropic elliptic problems. 2009. ⟨hal-00371443v2⟩