M. Feischl, T. Führer, M. Karkulik, J. Melenk, D. Praetorius:

"Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, Part I: Weakly-singular integral equation";

in: "ASC Report 24/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 26.

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

http://www.asc.tuwien.ac.at/preprint/2013/asc24x2013.pdf

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