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Duality Based A Posteriori Error Estimation for Quasi-Periodic Solutions Using Time Averages

Braack, M; Burman, E; Taschenberger, N; (2011) Duality Based A Posteriori Error Estimation for Quasi-Periodic Solutions Using Time Averages. SIAM Journal on Scientific Computing , 33 (5) 2199 - 2216. 10.1137/100809519. Green open access

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Abstract

We propose an a posteriori error estimation technique for the computation of average functionals of solutions for nonlinear time dependent problems based on duality techniques. The exact solution is assumed to have a periodic or quasi-periodic behavior favoring a fixed mesh strategy in time. We show how to circumvent the need of solving time dependent dual problems. The estimator consists of an averaged residual weighted by sensitivity factors coming from a stationary dual problem and an additional averaging error term coming from nonlinearities of the operator considered. In order to illustrate this technique the resulting adaptive algorithm is applied to several model problems: a linear scalar parabolic problem with known exact solution, the nonsteady Navier–Stokes equations with known exact solution, and finally to the well-known benchmark problem for Navier–Stokes (flow behind a cylinder) in order to verify the modeling assumptions.

Type: Article
Title: Duality Based A Posteriori Error Estimation for Quasi-Periodic Solutions Using Time Averages
Open access status: An open access version is available from UCL Discovery
DOI: 10.1137/100809519
Publisher version: http://dx.doi.org/10.1137/100809519
Language: English
Additional information: Copyright © 2011 Society for Industrial and Applied Mathematics
Keywords: error estimation, finite elements, adaptivity, fluid dynamics, Galerkin methods
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1384725
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