Repository: Freie Universität Berlin, Math Department

Duality based a posteriori error estimation for quasi periodic solutions using time averages

Braack, M. and Burman, E. and Taschenberger, N. (2011) Duality based a posteriori error estimation for quasi periodic solutions using time averages. SIAM J. Scientific Computing, 33 (10.1137/100809519). pp. 2199-2216. ISSN print: 1064-8275; online: 1095-7197

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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.

Item Type:Article
Uncontrolled Keywords:error estimation, finite elements, adaptivity, fluid dynamics, Galerkin methods
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:1156
Deposited By: Ulrike Eickers
Deposited On:22 Aug 2012 14:15
Last Modified:23 Aug 2012 12:34

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