Maximum norm a posteriori error estimate for a 2D singularly perturbed semilinear reaction-diffusion problem

被引：26

作者：

Kopteva, Natalia ^{[1
]}

机构：

[1] Univ Limerick, Dept Math & Stat, Limerick, Ireland

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2008年 / 46卷 / 03期

关键词：

reaction-diffusion; singular perturbation; a posteriori error estimate; maximum norm; no mesh aspect ratio condition; finite differences; layer-adapted mesh;

D O I：

10.1137/060677616

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A singularly perturbed semilinear reaction-diffusion equation, posed in the unit square, is discretized on arbitrary nonuniform tensor-product meshes. We establish a second- order maximum norm a posteriori error estimate that holds true uniformly in the small diffusion parameter. No mesh aspect ratio assumption is made. Numerical results are presented that support our theoretical estimate.

引用

页码：1602 / 1618

页数：17

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