Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems

被引：43

作者：

Roos, Hans-Goerg ^{[1
]}

Schopf, Martin ^{[1
]}

机构：

[1] Tech Univ Dresden, D-01062 Dresden, Germany

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2015年 / 95卷 / 06期

关键词：

Continuous interior penalty; FEM; reaction-diffusion; singularly perturbed;

D O I：

10.1002/zamm.201300226

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Error estimates of finite element methods for reaction-diffusion problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the H-1 seminorm leads to a balanced norm which reflects the layer behavior correctly. We prove error estimates in balanced norms and investigate also stability questions. Especially, we propose a new C-0 interior penalty method with improved stability properties in comparison with the Galerkin FEM. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：551 / 565

页数：15

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