A discrete collocation method for a hypersingular integral equation on curves with corners

Research output: Chapter in book/report/conference proceedingContribution to book/anthologyResearchpeer review

Authors

  • Thomas Hartmann
  • Ernst P. Stephan

Research Organisations

External Research Organisations

  • Ulm University of Applied Sciences
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Details

Original languageEnglish
Title of host publicationContemporary Computational Mathematics
Subtitle of host publicationA Celebration of the 80th Birthday of Ian Sloan
PublisherSpringer International Publishing AG
Pages545-566
Number of pages22
ISBN (electronic)9783319724560
ISBN (print)9783319724553
Publication statusPublished - 2018

Abstract

This paper is devoted to the approximate solution of a hypersingular integral equation on a closed polygonal boundary in ℝ2. We propose a fully discrete method with a trial space of trigonometric polynomials, combined with a trapezoidal rule approximation of the integrals. Before discretization the equation is transformed using a nonlinear (mesh grading) parametrization of the boundary curve which has the effect of smoothing out the singularities at the corners and yields fast convergence of the approximate solutions. The convergence results are illustrated with some numerical examples.

ASJC Scopus subject areas

Cite this

A discrete collocation method for a hypersingular integral equation on curves with corners. / Hartmann, Thomas; Stephan, Ernst P.
Contemporary Computational Mathematics: A Celebration of the 80th Birthday of Ian Sloan. Springer International Publishing AG, 2018. p. 545-566.

Research output: Chapter in book/report/conference proceedingContribution to book/anthologyResearchpeer review

Hartmann, T & Stephan, EP 2018, A discrete collocation method for a hypersingular integral equation on curves with corners. in Contemporary Computational Mathematics: A Celebration of the 80th Birthday of Ian Sloan. Springer International Publishing AG, pp. 545-566. https://doi.org/10.1007/978-3-319-72456-0_25
Hartmann, T., & Stephan, E. P. (2018). A discrete collocation method for a hypersingular integral equation on curves with corners. In Contemporary Computational Mathematics: A Celebration of the 80th Birthday of Ian Sloan (pp. 545-566). Springer International Publishing AG. https://doi.org/10.1007/978-3-319-72456-0_25
Hartmann T, Stephan EP. A discrete collocation method for a hypersingular integral equation on curves with corners. In Contemporary Computational Mathematics: A Celebration of the 80th Birthday of Ian Sloan. Springer International Publishing AG. 2018. p. 545-566 doi: 10.1007/978-3-319-72456-0_25
Hartmann, Thomas ; Stephan, Ernst P. / A discrete collocation method for a hypersingular integral equation on curves with corners. Contemporary Computational Mathematics: A Celebration of the 80th Birthday of Ian Sloan. Springer International Publishing AG, 2018. pp. 545-566
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