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Talks and Poster Presentations (without Proceedings-Entry):

M. Aurada, M. Feischl, S. Ferraz-Leite, M. Karkulik, C. Ortner, D. Praetorius:
"Adaptive mesh-refinement for Galerkin schemes: Simple h-h/2 error estimators and convergence";
Keynote Lecture: Mathematisches Kolloquium des Instituts für Angewandte Mathematik der Humboldt-Universität zu Berlin, Berlin (invited); 04-11-2012.



English abstract:
The (h-h/2)-strategy is one very basic and well-known technique for
the aposteriori error estimation. Let H be the energy space, which
is assumed to be a Hilbert space. Let u denote the exact solution.
One then considers

eta = || u_{h} - u_{h/2} ||

to estimate the error ||u-u_{h}||, where u_{h} is a Galerkin solution
with respect to a mesh T_{h} and u_{h/2} is a Galerkin solution for
a mesh T_{h/2} obtained from a uniform refinement of T_{h}.

We stress that eta always provides a lower bound for the Galerkin
error (efficiency), whereas the upper bound (reliability) is essentially
equivalent to a saturation assumption.

For several benchmark examples in FEM, BEM, and the FEM-BEM
coupling, we provide variants mu of eta, which are capable to steer
an adaptive mesh-refining algorithm. Moreover, by use of the
estimator reduction concept, one can prove that mu is driven to zero.
The developed adaptive schemes are simple in the sense that there
is almost no implementational overhead for the realization of the
refinement indicators.