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Keywords:
singular perturbation; finite element method; layer-adapted mesh; balanced norm
singular perturbation; finite element method; layer-adapted mesh; balanced norm
Summary:
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.
References:
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