C. Erath, S. Ferraz-Leite, S. Funken, D. Praetorius:
"Energy Norm Based A Posteriori Error Estimation for Boundary Element Methods in Two Dimensions";
Applied Numerical Mathematics, 59 (2009), S. 2713 - 2734.

Kurzfassung englisch:
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 2009], the two-level error estimator from
[Mund, Stephan, Weisse 1998], and the averaging error estimator from
[Carstensen, Praetorius 2006]. 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
examples, we consider first-kind integral equations in 2D with
weakly singular integral kernel.

boundary element method, a posteriori error estimate, adaptive mesh-refinement

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