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Adaptive boundary-element methods for transmission problems

Published online by Cambridge University Press:  17 February 2009

Carsten Carstensen  and
Ernst P. Stephan
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Abstract

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In this paper we present an adaptive boundary-element method for a transmission prob-lem 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.

Type
Research Article
Information
The ANZIAM Journal , Volume 38 , Issue 3 , January 1997 , pp. 336 - 367
Copyright
Copyright © Australian Mathematical Society 1997

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