On the Convergence of a Multigrid Method for Linear Reaction-Diffusion Problems |
| |
Authors: | Maxim A Olshanskii Arnold Reusken |
| |
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 |
| |
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 |
| |
Keywords: | AMS Subject Classifications: 65N22 65N30 65N55 |
本文献已被 SpringerLink 等数据库收录! |