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Convergence of some adaptive FEM-BEM coupling for elliptic butpossibly nonlinear interface problems

Published online by Cambridge University Press:  13 February 2012

Markus Aurada,
Michael Feischl and
Dirk Praetorius
Markus Aurada
Affiliation:
Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Wien, Austria. Markus.Aurada@tuwien.ac.at; Michael.Feischl@tuwien.ac.at; Dirk.Praetorius@tuwien.ac.at
Michael Feischl
Affiliation:
Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Wien, Austria. Markus.Aurada@tuwien.ac.at; Michael.Feischl@tuwien.ac.at; Dirk.Praetorius@tuwien.ac.at
Dirk Praetorius
Affiliation:
Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Wien, Austria. Markus.Aurada@tuwien.ac.at; Michael.Feischl@tuwien.ac.at; Dirk.Praetorius@tuwien.ac.at

Abstract

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We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear)interface problem for the 2D Laplacian. We introduce some new a posteriorierror estimators based on the (h − h/2)-errorestimation strategy. In particular, these include the approximation error for the boundarydata, which allows to work with discrete boundary integral operators only. Using theconcept of estimator reduction, we prove that the proposed adaptive algorithm isconvergent in the sense that it drives the underlying error estimator to zero. Numericalexperiments underline the reliability and efficiency of the considered adaptivemesh-refinement.

Keywords

FEM-BEM couplinga posteriori error estimateadaptive algorithmconvergence

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 5 , September 2012, pp. 1147 - 1173
Copyright
© EDP Sciences, SMAI, 2012

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