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S. Ferraz-Leite, C. Ortner, D. Praetorius:
"Convergence of adaptive Galerkin schemes steered by h-h/2-based error estimators";
Talk: SDIDE - Stability and Discretization Issues in Differential Equations, Wien (invited); 09-17-2008 - 09-21-2008.

We consider Galerkin discretizations of elliptic problems stated in
variational form in a Hilbert space setting. Based on the
$h$-$h/2$-error estimation strategy, we introduce an adaptive
algorithm which is proven to be convergent under the saturation
assumption. The developed adaptive scheme is simple in the sense
that there is almost no implementational overhead for the realization of the refinement indicators. This is very much
different for, e.g., residual-based indicators, which have been
treated in the literature so far. Besides finite element methods,
our framework applies to boundary integral formulations and yields
a first convergence proof for adaptive boundary element schemes.