Exponential convergence of the hp-version for the boundary element method on open surfaces |
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Authors: | Norbert Heuer Matthias Maischak Ernst P Stephan |
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Institution: | (1) Institut für Wissenschaftliche Datenverarbeitung, University of Bremen, D-28334 Bremen, Germany , DE;(2) Institut für Angewandte Mathematik, University of Hannover, Welfengarten 1, D-30167 Hannover, Germany , DE |
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Abstract: | Summary. We analyze the boundary element Galerkin method for weakly singular and hypersingular integral equations of the first kind
on open surfaces. We show that the hp-version of the Galerkin method with geometrically refined meshes converges exponentially
fast for both integral equations. The proof of this fast convergence is based on the special structure of the solutions of
the integral equations which possess specific singularities at the corners and the edges of the surface. We show that these
singularities can be efficiently approximated by piecewise tensor products of splines of different degrees on geometrically
graded meshes. Numerical experiments supporting these results are presented.
Received December 19, 1996 / Revised version received September 24, 1997 / Published online August 19, 1999 |
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Keywords: | Mathematics Subject Classification (1991):65N38 65R20 45L10 |
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