M. Aurada, S. Ferraz-Leite, D. Praetorius:
"Estimator reduction and convergence of adaptive BEM";
Applied Numerical Mathematics, 62 (2012), 6; S. 787 - 801.

Kurzfassung englisch:
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 Dörfler 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.

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