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A Nyström method for a boundary integral equation related to the Dirichlet problem on domains with corners

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Abstract

The authors consider the interior Dirichlet problem for Laplace’s equation on planar domains with corners. They provide a complete analysis of a natural method of Nyström type based on the global Gauss–Lobatto quadrature rule, in order to approximate the solution of the corresponding double layer boundary integral equation. Mellin-type integral operators are involved and, as usual, a modification of the method close to the corners is needed. A new modification is proposed and the convergence and stability of the “modified” quadrature method are proved. Some numerical tests are also included.

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Acknowledgments

The authors would like to thank the referee for the thorough review and the constructive suggestions which have helped to improve the contents of the paper.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Cagliari, Viale Merello 92, 09123, Cagliari, Italy

    Luisa Fermo

  2. Department of Mathematics, Computer Science and Economics, University of Basilicata, Via dell’Ateneo Lucano 10, 85100, Potenza, Italy

    Concetta Laurita

Authors
  1. Luisa Fermo
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  2. Concetta Laurita
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Correspondence to Concetta Laurita.

Additional information

The second author is partly supported by GNCS Project 2013 “Metodi fast per la risoluzione numerica di sistemi di equazioni integro-differenziali”.

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Fermo, L., Laurita, C. A Nyström method for a boundary integral equation related to the Dirichlet problem on domains with corners. Numer. Math. 130, 35–71 (2015). https://doi.org/10.1007/s00211-014-0657-6

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  • DOI: https://doi.org/10.1007/s00211-014-0657-6

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