Residual-based a posteriori error estimate for hypersingular equation on surfaces (original) (raw)

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
  2. M. Maischak
  3. D Praetorius
  4. E.P. Stephan

Corresponding author

Correspondence toCarsten 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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