Convergence estimates for multigrid algorithms without regularity assumptions

Bramble, James H.; Pasciak, Joseph E.; Wang, Jun Ping; Xu, Jinchao

doi:10.1090/S0025-5718-1991-1079008-4

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

Convergence estimates for multigrid algorithms without regularity assumptions

Authors: James H. Bramble, Joseph E. Pasciak, Jun Ping Wang and Jinchao Xu
Journal: Math. Comp. 57 (1991), 23-45
MSC: Primary 65J10; Secondary 65N55
MathSciNet review: 1079008
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Abstract | References | Similar Articles | Additional Information

Abstract: A new technique for proving rate of convergence estimates of multigrid algorithms for symmetric positive definite problems will be given in this paper. The standard multigrid theory requires a "regularity and approximation" assumption. In contrast, the new theory requires only an easily verified approximation assumption. This leads to convergence results for multigrid refinement applications, problems with irregular coefficients, and problems whose coefficients have large jumps. In addition, the new theory shows why it suffices to smooth only in the regions where new nodes are being added in multigrid refinement applications.

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