An asymptotic preserving scheme for strongly anisotropic elliptic problems

TL;DR

This paper presents an asymptotic preserving numerical scheme for efficiently solving strongly anisotropic elliptic equations in two dimensions, maintaining accuracy across all anisotropy ratios.

Contribution

The authors introduce a novel scheme that accurately solves anisotropic elliptic problems regardless of the anisotropy strength, improving upon existing methods.

Findings

The scheme effectively handles large anisotropy ratios.

It provides accurate solutions aligned with the anisotropy direction.

The method is applicable to problems with Neumann boundary conditions.

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.