Finite elements scheme in enriched subspaces for singularly perturbed reaction-diffusion problems on a square domain

被引：0
作者：
Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, United States [1 ]
不详 [2 ]
机构：
[1] Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington
[2] Division of Applied Mathematics, Brown University, Providence, RI 02912
来源：
Asymptotic Anal | 2008年 / 1-2卷 / 41-69期
关键词：
Boundary layers; Enriched subspaces; Finite elements; Reaction-diffusion; Singularly perturbed problem;
D O I：
10.3233/asy-2008-0865
中图分类号：
学科分类号：
摘要：
In this article, we discuss reaction-diffusion problems which produce ordinary boundary layers and elliptic corner layers. Using the classical polynomial Q1-finite elements spaces enriched with the so-called boundary layer elements which absorb the singularities due to the boundary and corner layers we are able to attain high numerical accuracies. We essentially obtain ε-uniform approximation errors in a weighted energy norm with significant simplifications in the numerical implementations; here we do not use mesh refinements.
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页码：41 / 69
页数：28
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