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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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1609-9389
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Volume 13, Issue 3 (Jul 2013)

Issues

Efficiency and Optimality of Some Weighted-Residual Error Estimator for Adaptive 2D Boundary Element Methods

Markus Aurada
  • Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8–10, 1040 Wien, Austria
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/ Michael Feischl
  • Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8–10, 1040 Wien, Austria
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/ Thomas Führer
  • Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8–10, 1040 Wien, Austria
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/ Michael Karkulik / Dirk Praetorius
  • Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8–10, 1040 Wien, Austria
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Published Online: 2013-07-02 | DOI: https://doi.org/10.1515/cmam-2013-0010

Abstract.

We prove convergence and quasi-optimality of a lowest-order adaptive boundary element method for a weakly-singular integral equation in 2D. The adaptive mesh-refinement is driven by the weighted-residual error estimator. By proving that this estimator is not only reliable, but under some regularity assumptions on the given data also efficient on locally refined meshes, we characterize the approximation class in terms of the Galerkin error only. In particular, this yields that no adaptive strategy can do better, and the weighted-residual error estimator is thus an optimal choice to steer the adaptive mesh-refinement. As a side result, we prove a weak form of the saturation assumption.

Keywords: Boundary Element Method; Weakly-Singular Integral Equation; A Posteriori Error Estimate; Adaptive Algorithm; Convergence; Optimality

About the article

Published Online: 2013-07-02

Published in Print: 2013-07-01


Citation Information: Computational Methods in Applied Mathematics, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2013-0010.

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© 2013 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

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