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Residual-based a posteriori error estimate for hypersingular equation on surfaces

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Summary.

The hypersingular integral equation of the first kind equivalently describes screen and Neumann problems on an open surface piece. The paper establishes a computable upper error bound for its Galerkin approximation and so motivates adaptive mesh refining algorithms. Numerical experiments for triangular elements on a screen provide empirical evidence of the superiority of adapted over uniform mesh-refining. The numerical realisation requires the evaluation of the hypersingular integral operator at a source point; this and other details on the algorithm are included.

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Authors and Affiliations

  1. Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Wiedner Hauptstrasse 8-10/115, 1040, Wien, Austria

    Carsten Carstensen & D Praetorius

  2. Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    M. Maischak & E.P. Stephan

Authors
  1. Carsten Carstensen
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  2. M. Maischak
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  3. D Praetorius
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  4. E.P. Stephan
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Correspondence to Carsten Carstensen.

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Mathematics Subject Classification (1991):65N30, 65R20, 73C50

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Carstensen, C., Maischak, M., Praetorius, D. et al. Residual-based a posteriori error estimate for hypersingular equation on surfaces. Numer. Math. 97, 397–425 (2004). https://doi.org/10.1007/s00211-003-0506-5

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  • DOI: https://doi.org/10.1007/s00211-003-0506-5

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