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The hp-version of the boundary element method with quasi-uniform meshes in three dimensions

Published online by Cambridge University Press:  04 July 2008

Alexei Bespalov  and
Norbert Heuer
Alexei Bespalov
Affiliation:
Department of Mathematical Sciences, Brunel University, Uxbridge, West London UB8 3PH, UK. albespalov@yahoo.com; norbert.heuer@gmail.com
Norbert Heuer
Affiliation:
Department of Mathematical Sciences, Brunel University, Uxbridge, West London UB8 3PH, UK. albespalov@yahoo.com; norbert.heuer@gmail.com
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Abstract

We prove an a priori error estimate for the hp-version of the boundary element method with hypersingular operators on piecewise plane open or closed surfaces. The underlying meshes are supposed to be quasi-uniform. The solutions of problems on polyhedral or piecewise plane open surfaces exhibit typical singularities which limit the convergence rate of the boundary element method. On closed surfaces, and for sufficiently smooth given data, the solution is H1-regular whereas, on open surfaces, edge singularities are strong enough to prevent the solution from being in H1. In this paper we cover both cases and, in particular, prove an a priori error estimate for the h-version with quasi-uniform meshes. For open surfaces we prove a convergence like O(h1/2p-1), h being the mesh size and p denoting the polynomial degree. This result had been conjectured previously.

Keywords

hp-version with quasi-uniform meshesboundary element methodsingularities.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 5 , September 2008 , pp. 821 - 849
Copyright
© EDP Sciences, SMAI, 2008

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