Analysis of V-Cycle Multigrid Algorithms for Forms Defined by Numerical Quadrature

The authors describe and analyze certain V-cycle multigrid algorithms with forms defined by numerical quadrature applied to the approximation of symmetric second-order elliptic boundary value problems. This approach can be used for the efficient solution of finite element systems resulting from nume...

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Veröffentlicht in:SIAM journal on scientific computing Jg. 15; H. 3; S. 566 - 576
Hauptverfasser: Bramble, J. H., Goldstein, C. I., Pasciak, J. E.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Society for Industrial and Applied Mathematics 01.05.1994
Schlagworte:
Algorithms
Applied mathematics
Approximation
Boundary value problems
Finite element analysis
ISSN:1064-8275, 1095-7197
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Zusammenfassung:The authors describe and analyze certain V-cycle multigrid algorithms with forms defined by numerical quadrature applied to the approximation of symmetric second-order elliptic boundary value problems. This approach can be used for the efficient solution of finite element systems resulting from numerical quadrature as well as systems arising from finite difference discretizations. The results are based on a regularity free theory and hence apply to meshes with local grid refinement as well as the quasi-uniform case. It is shown that uniform (independent of the number of levels) convergence rates often hold for appropriately defined V-cycle algorithms with as few as one smoothing per grid. These results hold even on applications without full elliptic regularity, e.g., a domain in $R^2 $ with a crack.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1064-8275
1095-7197
DOI:10.1137/0915037