On the Convergence of a Multigrid Method for Linear Reaction-Diffusion Problems |
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Authors: | Maxim A. Olshanskii Arnold Reusken |
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Affiliation: | (1) Department of Mechanics and Mathematics Moscow State University Moscow 119899 Russia e-mail: ay@olshan.msk.ru, RU;(2) Institut für Geometrie und Praktische Mathematik RWTH Aachen, Templergraben 55 D-52056 Aachen, Germany e-mail: reusken@igpm.rwth-aachen.de, DE |
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Abstract: | In this note we consider discrete linear reaction-diffusion problems. For the discretization a standard conforming finite element method is used. For the approximate solution of the resulting discrete problem a multigrid method with a damped Jacobi or symmetric Gauss-Seidel smoother is applied. We analyze the convergence of the multigrid V- and W-cycle in the framework of the approximation- and smoothing property. The multigrid method is shown to be robust in the sense that the contraction number can be bounded by a constant smaller than one which does not depend on the mesh size or on the diffusion-reaction ratio. Received June 15, 2000 |
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Keywords: | AMS Subject Classifications: 65N22, 65N30, 65N55. |
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