Publications in Scientific Journals:
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),
2713
- 2734.
English abstract:
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.
Keywords:
boundary element method, a posteriori error estimate, adaptive mesh-refinement
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1016/j.apnum.2008.12.024
Electronic version of the publication:
http://dx.doi.org/10.1016/j.apnum.2008.12.024
Created from the Publication Database of the Vienna University of Technology.