Numerische Mathematik

, Volume 132, Issue 3, pp 541–567

Adaptive boundary element methods for optimal convergence of point errors

  • Michael Feischl
  • Gregor Gantner
  • Alexander Haberl
  • Dirk Praetorius
  • Thomas Führer
Article

Abstract

One particular strength of the boundary element method is that it allows for a high-order pointwise approximation of the solution of the related partial differential equation via the representation formula. However, the high-order convergence and hence accuracy usually suffers from singularities of the Cauchy data. We propose two adaptive mesh-refining algorithms and prove their quasi-optimal convergence behavior with respect to an a posteriori computable bound for the point error in the representation formula. Numerical examples for the weakly-singular integral equations for the 2D and 3D Laplacian underline our theoretical findings.

Mathematics Subject Classification

65N38 65N50 41A25 65Y20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Michael Feischl
    • 1
  • Gregor Gantner
    • 1
  • Alexander Haberl
    • 1
  • Dirk Praetorius
    • 1
  • Thomas Führer
    • 2
  1. 1.Institute for Analysis and Scientific ComputingVienna University of TechnologyViennaAustria
  2. 2.Facultad de MatemáticasPontificia Universidad Católica de ChileSantiagoChile

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