Accessible Requires Authentication Published by De Gruyter May 28, 2014

A posteriori control of modelling and discretization errors for quasi periodic solutions

M. Braack and N. Taschenberger

Abstract

We propose a duality based a posteriori error estimator for the computation of functionals averaged in time for nonlinear time dependent problems. Such functionals are typically relevant for (quasi-)periodic solutions in time. Applications arise, e.g. in chemical reaction models. In order to reduce the numerical complexity, we use simultaneously locally refined meshes and adaptive (chemical) models. Hence, considerations of adjoint problems measuring the sensitivity of the functional output are needed. In contrast to the classical dual-weighted residual (DWR) method, we favor a fixed mesh and model strategy in time. Taking advantage of the (quasi-)periodic behaviour, only stationary dual problems have to be solved.

Published Online: 2014-5-28
Published in Print: 2014-6-1

© 2014 by Walter de Gruyter Berlin/Boston