An asymptotic preserving scheme for strongly anisotropic elliptic problems

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.

21 pages

References in corpus (1)

• An Asymptotic Preserving Scheme for the Euler equations in a strong magnetic field

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