The p-version of the boundary element method for weakly singular operators on piecewise plane open surfaces |
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Authors: | Alexei Bespalov Norbert Heuer |
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Affiliation: | (1) Computational Centre, Far-Eastern Branch of the Russian Academy of Sciences, Khabarovsk, Russia;(2) BICOM, Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK |
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Abstract: | We study piecewise polynomial approximations in negative order Sobolev norms of singularities which are inherent to Neumann data of elliptic problems of second order in polyhedral domains. The worst case of exterior crack problems in three dimensions is included. As an application, we prove an optimal a priori error estimate for the p-version of the BEM with weakly singular operators on polyhedral Lipschitz surfaces and piecewise plane open screens. The work of A. Bespalov was supported by the London Mathematical Society. The work of N. Heuer was supported by the FONDAP Programme in Applied Mathematics and Fondecyt project no. 1040615, both Chile. Dedicated to Professor Wolfgang L. Wendland on the occasion of his 70th birthday. |
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Keywords: | 41A10 65N15 65N38 |
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