Summary.
We prove an optimal a priori error estimate for the p-version of the boundary element method with hypersingular operators on piecewise plane open surfaces. The solutions of problems on open surfaces typically exhibit a singular behavior at the edges and corners of the surface which prevent an approximation analysis in H1. We analyze the approximation by polynomials of typical singular functions in fractional order Sobolev spaces thus giving, as an application, the optimal rate of convergence of the p-version of the boundary element method. This paper extends the results of [C. Schwab, M. Suri, The optimal p-version approximation of singularities on polyhedra in the boundary element method, SIAM J. Numer. Anal., 33 (1996), pp. 729–759] who only considered closed surfaces where the solution is in H1.
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Mathematics Subject Classification (2000): 41A10, 65N15, 65N38
Financed by the FONDAP Program in Applied Mathematics, Chile.
Supported by the FONDAP Program in Applied Mathematics and Fondecyt project no. 1010220, both Chile.
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Bespalov, A., Heuer, N. The p-version of the boundary element method for hypersingular operators on piecewise plane open surfaces. Numer. Math. 100, 185–209 (2005). https://doi.org/10.1007/s00211-005-0590-9
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DOI: https://doi.org/10.1007/s00211-005-0590-9