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

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

in: "ASC Report 30/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 22.

We analyze an adaptive boundary element method with fixed-order piecewise polynomials for the hyper-singular integral equation of the Laplace-Neumann problem in 2D and 3D which incorporates the approximation of the given Neumann data into the overall adaptive scheme. The adaptivity is driven by some residual-error estimator

plus data oscillation terms. We prove convergence even with quasi-optimal rates. Numerical experiments underline the theoretical results.

boundary element method, hyper-singular integral equation, a posteriori error estimate, adaptive algorithm, convergence, optimality

http://www.asc.tuwien.ac.at/preprint/2013/asc30x2013.pdf

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