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The optimal rate of convergence of the p-version of the boundary element method in two dimensions

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Summary.

We introduce the Jacobi-weighted Besov and Sobolev spaces in the one-dimensional setting. In the framework of these spaces, we analyze lower and upper bounds for approximation errors in the p-version of the boundary element method for hypersingular and weakly singular integral operators on polygons. We prove the optimal rate of convergence for the p-version in the energy norms of and respectively.

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Authors and Affiliations

  1. Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada

    Benqi Guo

  2. GI2 MA, Departamento de Ingenierí a Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Nobert Heuer

Authors
  1. Benqi Guo
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  2. Nobert Heuer
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Corresponding author

Correspondence to Benqi Guo.

Additional information

Mathematics Subject Classification (2000):  65N38

This author is supported by NSERC of Canada under Grant OGP0046726 and partially supported by the FONDAP Program (Chile) on Numerical Analysis during his visit of the Universidad de Concepción in 2001.

This author is supported by Fondecyt project no. 1010220 and by the FONDAP Program (Chile) on Numerical Analysis.

Revised version received January 28, 2004

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Guo, B., Heuer, N. The optimal rate of convergence of the p-version of the boundary element method in two dimensions. Numer. Math. 98, 499–538 (2004). https://doi.org/10.1007/s00211-004-0535-8

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  • DOI: https://doi.org/10.1007/s00211-004-0535-8

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