Maximum-norm error analysis of a non-monotone FEM for a singularly perturbed reaction-diffusion problem |
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Authors: | T Linss |
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Institution: | 1. Institut für Numerische Mathematik, Technische Universit?t Dresden, DE-01062, Dresden, Germany
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Abstract: | A non-monotone FEM discretization of a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits
strong layers is considered. The method is shown to be maximum-norm stable although it is not inverse monotone. Both a priori
and a posteriori error bounds in the maximum norm are derived. The a priori result can be used to deduce uniform convergence
of various layer-adapted meshes proposed in the literature. Numerical experiments complement the theoretical results.
AMS subject classification (2000) 65L10, 65L50, 65L60 |
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Keywords: | reaction-diffusion problems singular perturbation layer-adapted meshes |
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