TY  - JOUR
KW  - error estimation
KW  -  finite elements
KW  -  adaptivity
KW  -  fluid dynamics
KW  -  Galerkin methods
TI  - Duality Based A Posteriori Error Estimation for Quasi-Periodic Solutions Using Time Averages
UR  - http://dx.doi.org/10.1137/100809519
SP  - 2199 
VL  - 33
N2  - 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.
JF  - SIAM Journal on Scientific Computing
EP  -  2216
AV  - public
ID  - discovery1384725
SN  - 1064-8275
N1  - Copyright © 2011 Society for Industrial and Applied Mathematics
A1  - Braack, M
A1  - Burman, E
A1  - Taschenberger, N
Y1  - 2011/09/06/
IS  - 5
ER  -