Maximum norm a posteriori error estimates for a ID singularly perturbed semilinear reaction-diffusion problem

被引：31
|
作者：
Kopteva, Natalia [1 ]
机构：
[1] Univ Limerick, Dept Math Stat, Limerick, Ireland
来源：
IMA JOURNAL OF NUMERICAL ANALYSIS | 2007年 / 27卷 / 03期
基金：
爱尔兰科学基金会;
关键词：
reaction-diffusion; singular perturbation; finite differences; maximum norm; a posteriori error estimate; layer-adapted mesh; grid equidistribution;
D O I：
10.1093/imanum/drl020
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A singularly perturbed semilinear two-point boundary-value problem is discretized on arbitrary non-uniform meshes. We present second-order maximum norm a posteriori error estimates that hold true uniformly in the small parameter. Their application to monitor-function equidistribution and a posteriori mesh refinement are discussed. Numerical results are presented that support our theoretical estimates.
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页码：576 / 592
页数：17
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