Remarks on balanced norm error estimates for systems of reaction-diffusion equations

[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 discuss the difficulties which arise for systems of reaction-diffusion problems.

[学科分类] 应用数学

[关键词] singular perturbation;finite element method;layer-adapted mesh;balanced norm