Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor

Michael Feischl 1 , Thomas Führer 1 , Gregor Mitscha-Eibl 1 , Dirk Praetorius 1 ,  and Ernst P. Stephan 2
  • 1 Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8–10, 1040 Wien, Austria
  • 2 Institute for Applied Mathematics, Leibniz University Hannover, Welfengarten 1, 30167 Hannover, Germany

Abstract

We analyze adaptive mesh-refining algorithms in the frame of boundary element methods (BEM) and the coupling of finite elements and boundary elements (FEM-BEM). Adaptivity is driven by the two-level error estimator proposed by Ernst P. Stephan, Norbert Heuer, and coworkers in the frame of BEM and FEM-BEM or by the residual error estimator introduced by Birgit Faermann for BEM for weakly-singular integral equations. We prove that in either case the usual adaptive algorithm drives the associated error estimator to zero. Emphasis is put on the fact that the error estimators considered are not even globally equivalent to weighted-residual error estimators for which recently convergence with quasi-optimal algebraic rates has been derived.

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CMAM considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. The journal is interdisciplinary while retaining the common thread of numerical analysis, readily readable and meant for a wide circle of researchers in applied mathematics.

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