C. Erath, S. Ferraz-Leite, S. Funken, D. Praetorius:

"Energy Norm Based A Posteriori Error Estimation for Boundary Element Methods in Two Dimensions";

in: "ASC Report 07/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

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

Galerkin boundary element computations. We analyze the mathematical relation

between the h-h/2-error estimator from [Ferraz-Leite, Praetorius 2007], the

two-level error estimator from [Mund, Stephan, Weisse 1998], and the averaging

error estimator from [Carstensen, Praetorius 2005]. We essentially show that

all of these are equivalent, and we extend the analysis of

[Mund, Stephan, Weisse 1998] to cover adaptive mesh-refinement.

Therefore, all error estimators give lower bounds for the Galerkin error,

whereas upper bounds depend crucially on the saturation assumption. As

model example serve first-kind integral equations in 2D with weakly singular

integral kernel.

http://www.asc.tuwien.ac.at/preprint/2007/asc07x2007.pdf

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