A multiplicative Schwarz adaptive wavelet method for elliptic boundary value problems
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- by Rob Stevenson and Manuel Werner;
- Math. Comp. 78 (2009), 619-644
- DOI: https://doi.org/10.1090/S0025-5718-08-02186-8
- Published electronically: November 13, 2008
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Abstract:
A multiplicative Schwarz overlapping domain decomposition method is considered for solving elliptic boundary value problems. By equipping the relevant Sobolev spaces on the subdomains with wavelet bases, adaptive wavelet methods are used for approximately solving the subdomain problems. The union of the wavelet bases forms a frame for the Sobolev space on the domain as a whole. The resulting method is proven to be optimal in the sense that, in linear complexity, the iterands converge with the same rate as the sequence over $N \in \mathbb {N}$ of the best approximation from the span of the best $N$ frame elements. Numerical results are given for the method applied to Poisson’s equation.References
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Bibliographic Information
- Rob Stevenson
- Affiliation: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
- MR Author ID: 310898
- Email: rstevens@science.uva.nl
- Manuel Werner
- Affiliation: Fachbereich 12 Mathematik und Informatik, Philipps–Universität Marburg, Hans–Meerwein–Strasse, Lahnberge, D–35032, Marburg, Germany
- Email: werner@mathematik.uni-marburg.de
- Received by editor(s): March 6, 2008
- Published electronically: November 13, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 78 (2009), 619-644
- MSC (2000): Primary 65N55, 65T60, 41A25
- DOI: https://doi.org/10.1090/S0025-5718-08-02186-8
- MathSciNet review: 2476554