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An a posteriori error estimate for a first-kind integral equation

Author: Carsten Carstensen
Journal: Math. Comp. 66 (1997), 139-155
MSC (1991): Primary 65N38, 65N15, 65R20, 45L10
MathSciNet review: 1372001
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Abstract: In this paper we present a new a posteriori error estimate for the boundary element method applied to an integral equation of the first kind. The estimate is local and sharp for quasi-uniform meshes and so improves earlier work of ours. The mesh-dependence of the constants is analyzed and shown to be weaker than expected from our previous work. Besides the Galerkin boundary element method, the collocation method and the qualocation method are considered. A numerical example is given involving an adaptive feedback algorithm.

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Carsten Carstensen
Affiliation: Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany

Keywords: Integral equations, boundary element method, a posteriori error estimate, adaptive algorithm, collocation method, qualocation method
Received by editor(s): February 20, 1995
Received by editor(s) in revised form: November 6, 1995, and January 26, 1996
Article copyright: © Copyright 1997 American Mathematical Society