The convergence rate of a multigrid method with Gauss-Seidel relaxation for the Poisson equation

Author:
Dietrich Braess

Journal:
Math. Comp. **42** (1984), 505-519

MSC:
Primary 65N20

DOI:
https://doi.org/10.1090/S0025-5718-1984-0736449-6

MathSciNet review:
736449

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Abstract: The convergence rate of a multigrid method for the numerical solution of the Poisson equation on a uniform grid is estimated. The results are independent of the shape of the domain as long as it is convex and polygonal. On the other hand, pollution effects become apparent when the domain contains reentrant corners. To estimate the smoothing of the Gauss-Seidel relaxation, the smoothness is measured by comparing the energy norm with a (weaker) discrete seminorm.

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DOI:
https://doi.org/10.1090/S0025-5718-1984-0736449-6

Article copyright:
© Copyright 1984
American Mathematical Society