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

Braack, Malte and Taschenberger, N. (2014) A posteriori control of modelling and discretization errors for quasi periodic solutions. Journal of Numerical Mathematics, 22 (2). pp. 87-108. DOI 10.1515/jnma-2014-0004.

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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.

Document Type: Article
Additional Information: Times Cited: 1 0 1
Keywords: a posteriori estimation; model adaptivity; duality; Galerkin methods Artikelinformationen
Research affiliation: Kiel University > Kiel Marine Science
OceanRep > The Future Ocean - Cluster of Excellence > FO-R11
OceanRep > The Future Ocean - Cluster of Excellence
Kiel University
Refereed: Yes
Open Access Journal?: No
DOI etc.: 10.1515/jnma-2014-0004
ISSN: 1570-2820
Projects: Future Ocean
Date Deposited: 30 Mar 2015 12:01
Last Modified: 23 Aug 2019 08:30
URI: http://oceanrep.geomar.de/id/eprint/27216

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