, Volume 51, Issue 4, pp 531–562 | Cite as

Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, part I: weakly-singular integral equation

  • Michael FeischlEmail author
  • Thomas Führer
  • Michael Karkulik
  • Jens Markus Melenk
  • Dirk Praetorius


We analyze an adaptive boundary element method for Symm’s integral equation in 2D and 3D which incorporates the approximation of the Dirichlet data \(g\) into the adaptive scheme. We prove quasi-optimal convergence rates for any \(H^{1/2}\)-stable projection used for data approximation.


Boundary element method Weakly-singular integral equation  A posteriori error estimate Adaptive algorithm  Convergence Optimality 

Mathematics Subject Classification

65N30 65N38 65N50 65R20 41A25 



The authors MF, TF, and DP acknowledge support through the Austrian Science Fund (FWF) under grant P21732 Adaptive Boundary Element Method. MK acknowledges support by CONICYT project Anillo ACT1118 (ANANUM). The authors MF, JMM and DP acknowledge the support of the FWF doctoral program “Dissipation and Dispersion in Nonlinear PDEs” under grant W1245.


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Copyright information

© Springer-Verlag Italia 2013

Authors and Affiliations

  • Michael Feischl
    • 1
    Email author
  • Thomas Führer
    • 1
  • Michael Karkulik
    • 2
  • Jens Markus Melenk
    • 1
  • Dirk Praetorius
    • 1
  1. 1.Institute for Analysis and Scientific ComputingVienna University of TechnologyViennaAustria
  2. 2.Departamento de MatemáticasPontificia Universidad Católica de ChileSantiagoChile

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