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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

4 Issues per year


IMPACT FACTOR 2016: 1.097

CiteScore 2016: 1.09

SCImago Journal Rank (SJR) 2016: 0.872
Source Normalized Impact per Paper (SNIP) 2016: 0.887

Mathematical Citation Quotient (MCQ) 2016: 0.75

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1609-9389
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Volume 14, Issue 4 (Oct 2014)

Issues

Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor

Michael Feischl
  • Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8–10, 1040 Wien, Austria
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/ Thomas Führer
  • Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8–10, 1040 Wien, Austria
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/ Gregor Mitscha-Eibl
  • Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8–10, 1040 Wien, Austria
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/ Dirk Praetorius
  • Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8–10, 1040 Wien, Austria
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/ Ernst P. Stephan
Published Online: 2014-07-03 | DOI: https://doi.org/10.1515/cmam-2014-0019

Abstract

We analyze adaptive mesh-refining algorithms in the frame of boundary element methods (BEM) and the coupling of finite elements and boundary elements (FEM-BEM). Adaptivity is driven by the two-level error estimator proposed by Ernst P. Stephan, Norbert Heuer, and coworkers in the frame of BEM and FEM-BEM or by the residual error estimator introduced by Birgit Faermann for BEM for weakly-singular integral equations. We prove that in either case the usual adaptive algorithm drives the associated error estimator to zero. Emphasis is put on the fact that the error estimators considered are not even globally equivalent to weighted-residual error estimators for which recently convergence with quasi-optimal algebraic rates has been derived.

Keywords: Boundary Element Method (BEM); FEM-BEM Coupling; A Posteriori Error Estimate; Adaptive Algorithm; Convergence

MSC: 65N12; 65N38; 65N30; 65N50

About the article

Received: 2014-05-30

Accepted: 2014-06-16

Published Online: 2014-07-03

Published in Print: 2014-10-01


Funding Source: Austrian Science Fund (FWF)

Award identifier / Grant number: P21732

Funding Source: Austrian Science Fund (FWF)

Award identifier / Grant number: P27005

Funding Source: Vienna University of Technology

Award identifier / Grant number: Innovative projects initiative

Funding Source: FWF Doctoral Program

Award identifier / Grant number: W1245


Citation Information: Computational Methods in Applied Mathematics, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2014-0019.

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[1]
Gregor Mitscha-Baude, Andreas Buttinger-Kreuzhuber, Gerhard Tulzer, and Clemens Heitzinger
Journal of Computational Physics, 2017, Volume 338, Page 452
[2]
Michael Feischl, Gregor Gantner, Alexander Haberl, and Dirk Praetorius
Numerische Mathematik, 2017, Volume 136, Number 1, Page 147
[3]
Michael Feischl, Gregor Gantner, Alexander Haberl, and Dirk Praetorius
Engineering Analysis with Boundary Elements, 2016, Volume 62, Page 141
[4]
Michael Feischl, Gregor Gantner, and Dirk Praetorius
Computer Methods in Applied Mechanics and Engineering, 2015, Volume 290, Page 362

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