DUALITY BASED A POSTERIORI ERROR ESTIMATION FOR QUASI-PERIODIC SOLUTIONS USING TIME AVERAGES

Braack, M., Burman, E. and Taschenberger, N. (2011) DUALITY BASED A POSTERIORI ERROR ESTIMATION FOR QUASI-PERIODIC SOLUTIONS USING TIME AVERAGES Siam Journal on Scientific Computing, 33 (5). pp. 2199-2216. DOI 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.

Document Type: Article
Keywords: error estimation finite elements adaptivity fluid dynamics Galerkin methods
Research affiliation: Kiel University
Refereed: Yes
DOI etc.: 10.1137/100809519
ISSN: 1064-8275
Date Deposited: 01 Nov 2012 04:56
Last Modified: 01 Nov 2012 04:56
URI: http://eprints.uni-kiel.de/id/eprint/16872

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