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Convergence of some adaptive FEM-BEM coupling for elliptic but possibly 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
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Abstract

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 posteriori error estimators based on the (h − h/2)-error estimation strategy. In particular, these include the approximation error for the boundary data, which allows to work with discrete boundary integral operators only. Using the concept of estimator reduction, we prove that the proposed adaptive algorithm is convergent in the sense that it drives the underlying error estimator to zero. Numerical experiments underline the reliability and efficiency of the considered adaptive mesh-refinement.

Keywords

FEM-BEM couplinga posteriori error estimateadaptive algorithmconvergence
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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