An Asymptotic Preserving Scheme for Strongly Anisotropic Elliptic Problems

Pierre Degond, Fabrice Deluzet, Claudia Negulescu

Type: Article

Publication Date: 2010-01-01

Citations: 47

DOI: https://doi.org/10.1137/090754200

Abstract

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.

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