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Local, Residual-Based A Posteriori Error Estimates Forcing Adaptive Boundary Element Methods

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Boundary Element Topics

Abstract

The aim of this contribution is to prove local residual-based a posteriori error estimates for a wide class of nonlocal operators arising in the boundary element method corresponding to the Galerkin discretization scheme. First results of this type were proved by Saranen [14, 15], Saranen and Wendland [16] and Wendland and Yu [25]. These results provide estimates only on fixed parts of the boundary surface, which is not appropriate for adaptive methods. Here we present a new result to overcome this disadvantage and present for the first time local a posteriori error bounds. Furthermore we present a new technique to calculate Sobolev norms with non-integer Sobolev indices based on a window technique.

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Authors
  1. H. Schulz
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  2. W. L. Wendland
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Editor information

Editors and Affiliations

  1. Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, D-70569, Stuttgart, Germany

    Wolfgang L. Wendland

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© 1997 Springer-Verlag Berlin Heidelberg

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Schulz, H., Wendland, W.L. (1997). Local, Residual-Based A Posteriori Error Estimates Forcing Adaptive Boundary Element Methods. In: Wendland, W.L. (eds) Boundary Element Topics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60791-2_21

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  • DOI: https://doi.org/10.1007/978-3-642-60791-2_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64554-9

  • Online ISBN: 978-3-642-60791-2

  • eBook Packages: Springer Book Archive

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