A posteriori error estimate and h-adaptive algorithm on surfaces for Symm's integral equation (original) (raw)

Summary.

A residual-based a posteriori error estimate for boundary integral equations on surfaces is derived in this paper. A localisation argument involves a Lipschitz partition of unity such as nodal basis functions known from finite element methods. The abstract estimate does not use any property of the discrete solution, but simplifies for the Galerkin discretisation of Symm's integral equation if piecewise constants belong to the test space. The estimate suggests an isotropic adaptive algorithm for automatic mesh-refinement. An alternative motivation from a two-level error estimate is possible but then requires a saturation assumption. The efficiency of an anisotropic version is discussed and supported by numerical experiments.

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Authors and Affiliations

  1. Mathematical Seminar, University of Kiel, Ludwig-Meyn-Strasse 4, 24098 Kiel, Germany; e-mail: cc@numerik.uni-kiel.de, , , , , , DE
    C. Carstensen
  2. Institute for Applied Mathematics, University of Hannover, Welfengarten 1, 30167 Hannover, Germany; e-mail: {maischak,stephan}@ifam.uni-hannover.de, , , , , , DE
    M. Maischak & E.P. Stephan

Authors

  1. C. Carstensen
  2. M. Maischak
  3. E.P. Stephan

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Received November 29, 1999 / Revised version received August 10, 2000 / Published online May 30, 2001

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Carstensen, C., Maischak, M. & Stephan, E. A posteriori error estimate and h-adaptive algorithm on surfaces for Symm's integral equation.Numer. Math. 90, 197–213 (2001). https://doi.org/10.1007/s002110100287

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