Issue |
ESAIM: COCV
Volume 18, Number 4, October-December 2012
|
|
---|---|---|
Page(s) | 987 - 1004 | |
DOI | https://doi.org/10.1051/cocv/2011201 | |
Published online | 16 January 2012 |
Linear-quadratic optimal control for the Oseen equations with stabilized finite elements
Mathematisches Seminar,
Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098
Kiel,
Germany
braack@math.uni-kiel.de; tews@math.uni-kiel.de
Received:
26
November
2010
Revised:
15
September
2011
For robust discretizations of the Navier-Stokes equations with small viscosity, standard Galerkin schemes have to be augmented by stabilization terms due to the indefinite convective terms and due to a possible lost of a discrete inf-sup condition. For optimal control problems for fluids such stabilization have in general an undesired effect in the sense that optimization and discretization do not commute. This is the case for the combination of streamline upwind Petrov-Galerkin (SUPG) and pressure stabilized Petrov-Galerkin (PSPG). In this work we study the effect of different stabilized finite element methods to distributed control problems governed by singular perturbed Oseen equations. In particular, we address the question whether a possible commutation error in optimal control problems lead to a decline of convergence order. Therefore, we give a priori estimates for SUPG/PSPG. In a numerical study for a flow with boundary layers, we illustrate to which extend the commutation error affects the accuracy.
Mathematics Subject Classification: 35A15 / 49Mxx / 65G99 / 65M60 / 76D05 / 76D07 / 76D55
Key words: Oseen / Navier-Stokes / optimal control / finite elements / stabilized methods
© EDP Sciences, SMAI, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.