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The p-version of the boundary element method for weakly singular operators on piecewise plane open surfaces

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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.

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Authors and Affiliations

  1. Computational Centre, Far-Eastern Branch of the Russian Academy of Sciences, Khabarovsk, Russia

    Alexei Bespalov & Norbert Heuer

Authors
  1. Alexei Bespalov
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  2. Norbert Heuer
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Correspondence to Norbert Heuer.

Additional information

Dedicated to Professor Wolfgang L. Wendland on the occasion of his 70th birthday.

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.

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Bespalov, A., Heuer, N. The p-version of the boundary element method for weakly singular operators on piecewise plane open surfaces. Numer. Math. 106, 69–97 (2007). https://doi.org/10.1007/s00211-006-0058-6

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  • DOI: https://doi.org/10.1007/s00211-006-0058-6

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