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The optimal convergence of the h–p version of the boundary element method with quasiuniform meshes for elliptic problems on polygonal domains

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Abstract

In the framework of the Jacobi-weighted Besov spaces, we analyze the lower and upper bounds of errors in the h–p version of boundary element solutions on quasiuniform meshes for elliptic problems on polygons. Both lower bound and upper bound are optimal in h and p, and they are of the same order. The optimal convergence of the h–p version of boundary element method with quasiuniform meshes is proved, which includes the optimal rates for h version with quasiuniform meshes and the p version with quasiuniform degrees as two special cases.

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Authors and Affiliations

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

    Benqi Guo

  2. GI2MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla, 160-C, Concepción, Chile

    Norbert Heuer

Authors
  1. Benqi Guo
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  2. Norbert Heuer
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Correspondence to Benqi Guo.

Additional information

Communicated by Yuesheng Xu

Dedicated to Professor Charles Micchelli on the occasion of his sixtieth birthday

Mathematics subject classification (2000)

65N38.

Benqi Guo: The work of this author was supported by NSERC of Canada under Grant OGP0046726 and was complete during visiting Newton Institute for Mathematical Sciences, Cambridge University for participating in special program “Computational Challenges in PDEs” in 2003.

Norbert Heuer: This author is supported by Fondecyt project No. 1010220 and by the FONDAP Program (Chile) on Numerical Analysis. Current address: Mathematical Sciences, Brunel University, Uxbridge, U.K.

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Guo, B., Heuer, N. The optimal convergence of the h–p version of the boundary element method with quasiuniform meshes for elliptic problems on polygonal domains. Adv Comput Math 24, 353–374 (2006). https://doi.org/10.1007/s10444-004-7618-z

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  • DOI: https://doi.org/10.1007/s10444-004-7618-z

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