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Local Defect Correction Method and Domain Decomposition Techniques

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Defect Correction Methods

Part of the book series: Computing Supplementum ((COMPUTING,volume 5))

Abstract

For elliptic problems a local defect correction method is described. A basic (global) discretization is improved by a local discretization defined in a subdomain. The convergence rate of the local defect correction iteration is proved to be proportional to a certain positive power of the step size. The accuracy of the converged solution can be described. Numerical examples confirm the theoretical results. We discuss multi-grid iterations converging to the same solution.

The local defect correction determines a solution depending on one global and one or more local discretizations. An extension of this approach is the domain decomposition method, where only (overlapping) local problems are combined. Such a combination of local subproblems can be solved efficiently by a multi-grid iteration. We describe a multi-grid variant that is suited for the use of parallel processors.

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Author information

Authors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Christian-Albrechts-Universität, Olshausenstrasse 40, Kiel 1, D-2300, Federal Republic of Germany

    Dr. W. Hackbusch

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  1. Dr. W. Hackbusch
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik, Universität Marburg, Federal Republic of Germany

    Klaus Böhmer

  2. Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Austria

    Hans J. Stetter

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© 1984 Springer-Verlag

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Hackbusch, W. (1984). Local Defect Correction Method and Domain Decomposition Techniques. In: Böhmer, K., Stetter, H.J. (eds) Defect Correction Methods. Computing Supplementum, vol 5. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7023-6_6

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  • DOI: https://doi.org/10.1007/978-3-7091-7023-6_6

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81832-9

  • Online ISBN: 978-3-7091-7023-6

  • eBook Packages: Springer Book Archive

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