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.
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Received June 15, 2000
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Olshanskii, M., Reusken, A. On the Convergence of a Multigrid Method for Linear Reaction-Diffusion Problems. Computing 65, 193–202 (2000). https://doi.org/10.1007/s006070070006
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DOI: https://doi.org/10.1007/s006070070006