Two-level methods for the single layer potential in ?3 |
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Authors: | P Mund E P Stephan J Weiße |
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Affiliation: | 1. Institut für Angewandte Mathematik, Universit?t Hannover, Welfengarten 1, 30167, Hannover, Germany
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Abstract: | We consider weakly singular integral equations of the first kind on open surface pieces Γ in ℝ3. To obtain approximate solutions we use theh-version Galerkin boundary element method. Furthermore we introduce two-level additive Schwarz operators for non-overlapping
domain decompositions of Γ and we estimate the conditions numbers of these operators with respect to the mesh size. Based
on these operators we derive an a posteriori error estimate for the difference between the exact solution and the Galerkin
solution. The estimate also involves the error which comes from an approximate solution of the Galerkin equations. For uniform
meshes and under the assumption of a saturation condition we show reliability and efficiency of our estimate. Based on this
estimate we introduce an adaptive multilevel algorithm with easily computable local error indicators which allows direction
control of the local refinements. The theoretical results are illustrated by numerical examples for plane and curved surfaces.
Supported by the German Research Foundation (DFG) under grant Ste 238/25-9. |
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Keywords: | 65N38 65N55 |
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