97-10   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Birgit Faermann:

Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods

In this paper we show that the Aronszajn-Slobodeckij norm tex2html_wrap_inline11 (given by a double integral for a non-integer tex2html_wrap_inline13) is localizable. Using this result, we get new local a-posteriori error indicators for the Galerkin discretization of boundary integral equations. The error indicators are reliable for K-meshes and efficient for arbitrary meshes for a wide class of integral operators, in particular for operators of negative order. The error indicators are based on local norms of the computable residual and can be used for controlling the adaptive mesh refinement. Numerical examples confirm our theoretical results.

Mathematics Subject Classification (1991): 65N38, 65R20, 65N30, 65N15, 65N50, 65D07, 45B05, 45L10

Bibliographical note: IMA J. Numer. Anal. 20 2000, pp. 203-234.

Keywords: Integral equations, boundary element methods, Galerkin method, a-posteriori error estimate, adaptive mesh refinement

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[Thu Feb 19 18:56:33 2009]
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