J Austral Math Soc Ser B 38 pp336--367, 1997.

Adaptive boundary-element methods for transmission problems

Carsten Carstensen and Ernst P. Stephan

(Received 20 September 1993; revised 2 January 1995)

Abstract

In this paper we present an adaptive boundary-element method for a transmission problem for the Laplacian in a two-dimensional Lipschitz domain. We are concerned with an equivalent system of boundary-integral equations of the first kind (on the transmission boundary) involving weakly-singular, singular and hypersingular integral operators. For the h-version boundary-element (Galerkin) discretization we derive an a posteriori error estimate which guarantees a given bound for the error in the energy norm (up to a multiplicative constant). Then, following Eriksson and Johnson this yields an adaptive algorithm steering the mesh refinement. Numerical examples confirm that our adaptive algorithms yield automatically good triangulations and are efficient.

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Authors

The work is partly supported by DFG research group at the University of Hannover

Carsten Carstensen: Mathematics Seminar, Universität Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, FRG.
Ernst P. Stephan: Insitut für Angewandte Mathematik, UNI Hannover, D-30167 Hannover, FRG.

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Last Modified: Mon Dec 10 16:56:23 2001