Conference abstracts

Session B6 - Multiresolution and Adaptivity in Numerical PDEs - Semi-plenary talk

July 15, 17:00 ~ 17:50 - Room T1

Oscillation in a posteriori error estimation

Andreas Veeser

Universit√† degli Studi di Milano, Italy   -   andreas.veeser@unimi.it

In a posteriori error estimation, one devises computationally accessible estimators for the error of an approximate PDE solution. Such estimators allow evaluating the approximation quality and are also used to guide adaptive mesh refinement.

In the available approaches to a posteriori error estimation, the estimators are equivalent to the approximation error, up to so-called oscillation terms. These terms vanish for data resolved by the underlying mesh, but they can be arbitrarily bigger than the error. Oscillation was believed to be exclusively the price of (a better) computability and to converge at least as fast as the error. A remarkable example of Cohen, DeVore and Nochetto (2012) shows that both beliefs are wrong for the oscillation terms in the available approaches.

This talk presents a new approach to a posteriori error estimation and applications. In contrast to preceding ones, the arising, new oscillation terms are bounded by the error. The new twist is an interpolation operator that splits the residual into an approximate residual with oscillation-free data and second part concerning the not yet resolved data.

Joint work with Christian Kreuzer (Ruhr-Universität Bochum, Germany).

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