M. Aurada, S. Ferraz-Leite, D. Praetorius:

"Estimator reduction and convergence of adaptive BEM";

in: "ASC Report 09/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

A posteriori error estimation and related adaptive mesh-refining algorithms

have themselves proven to be powerful tools in nowadays scientific computing. Contrary

to adaptive finite element methods, convergence of adaptive boundary element schemes is,

however, widely open. We propose a relaxed notion of convergence of adaptive boundary

element schemes. Instead of asking for convergence of the error to zero, we only aim to prove

estimator convergence in the sense that the adaptive algorithm drives the underlying error

estimator to zero. We observe that certain error estimators satisfy an estimator reduction

property which is sufficient for estimator convergence. The elementary analysis is only

based on D¨orfler marking and inverse estimates, but not on reliability and efficiency of the

error estimator at hand. In particular, our approach gives a first mathematical justification

for the proposed steering of anisotropic mesh-refinements, which is mandatory for optimal

convergence behaviour in 3D boundary element computations.

http://www.asc.tuwien.ac.at/preprint/2010/asc09x2010.pdf

Created from the Publication Database of the Vienna University of Technology.