Adaptive BEM with optimal convergence rates for the Helmholtz equation

Alex Bespalov, Timo Betcke, Alexander Haberl, Dirk Praetorius

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
85 Downloads (Pure)


We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on any a priori information that the underlying meshes are sufficiently fine. We prove convergence of the error estimator with optimal algebraic rates, independently of the (coarse) initial mesh. As a technical contribution, we prove certain local inverse-type estimates for the boundary integral operators associated with the Helmholtz equation.
Original languageEnglish
Pages (from-to)260-287
Number of pages34
JournalComputer Methods in Applied Mechanics and Engineering
Early online date12 Dec 2018
Publication statusPublished - 1 Apr 2019


  • boundary element method
  • Helmholtz equation
  • a posteriori error estimate
  • adaptive algorithm
  • convergence
  • optimality


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