Parameter uniform approximations for time‐dependent reaction‐diffusion problems |
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| Authors: | Torsten Linß Niall Madden |
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| Institution: | 1. Institut für Numerische Mathematik, Technische Universit?t Dresden, D‐01062 Dresden, GermanyInstitut für Numerische Mathematik, Technische Universit?t Dresden, D‐01062 Dresden, Germany;2. Department of Mathematics, National University of Ireland, Galway, Ireland |
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| Abstract: | Using discrete Green's functions techniques, we present a classification of fitted mesh methods for time‐dependent reaction diffusion problems, based on the analyses of Linß (Linß, Numer Algor 40 (2005), 23–32) for the analogous steady‐state problem and of Kopteva (Kopteva, Computing 66 (2001), 179–197) for time‐dependent convection‐diffusion problems. As examples of how to apply the analysis, we derive error estimates for the fitted meshes of Shishkin and Bakhvalov, and provide supporting numerical results. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 |
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| Keywords: | singularly perturbed layer‐adapted meshes |
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