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The contraction number of a multigrid method for solving the Poisson equation

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Summary

The treatment of a multigrid method in the framework of numerical analysis elucidates that regularity of the solution is not necessary for the convergence of the multigrid algorithm but only for fast convergence. For the linear equations which arise from the discretization of the Poisson equation, a convergence factor 0,5 is established independent of the shape of the domain and of the regularity of the solution.

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Authors and Affiliations

  1. Institut für Mathematik, Ruhr-Universität Bochum, Universitätsstr. 150, D-4630, Bochum 1, Germany (Fed. Rep.)

    Dietrich Braess

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  1. Dietrich Braess
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Dedicated to Professor Dr.Dr.h.c. Lothar Collatz on the occasion of his 70 th birthday

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Braess, D. The contraction number of a multigrid method for solving the Poisson equation. Numer. Math. 37, 387–404 (1981). https://doi.org/10.1007/BF01400317

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  • DOI: https://doi.org/10.1007/BF01400317

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