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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The convergence rate of a multigrid method with Gauss-Seidel relaxation for the Poisson equation
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by Dietrich Braess PDF
Math. Comp. 42 (1984), 505-519 Request permission

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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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Math. Comp. 42 (1984), 505-519
  • MSC: Primary 65N20
  • DOI: https://doi.org/10.1090/S0025-5718-1984-0736449-6
  • MathSciNet review: 736449