C. Erath, S. Funken, P. Goldenits, D. Praetorius:

"Simple error estimators for the Galerkin BEM for some hypersingular integral equation in 2D";

in: "ASC Report 20/2009", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5.

A posteriori error estimation is an important tool for reliable and efficient

Galerkin boundary element computations. For hypersingular integral equations

in 2D with positive-order Sobolev space, we analyze the mathematical relation

between the (h-h/2)-error estimator from [Ferraz-Leite, Praetorius 2008], the

two-level error estimator from [Maischak, Mund, Stephan 1997], and the

averaging error estimator from [Carstensen, Praetorius 2008]. All of these

aposteriori error estimators are simple in the following sense: First, the

numerical analysis can be done within the same mathematical framework, namely

localization techniques for the energy norm. Second, there is almost no

implementational overhead for the realization. In particular, this is very

much different to other aposteriori error estimators proposed in the

literature. As model example serves the hypersingular integral equation

associated with the 2D Laplacian, and numerical experiments underline the

mathematical results.

http://www.asc.tuwien.ac.at/preprint/2009/asc20x2009.pdf

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