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.
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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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