LINEAR-QUADRATIC OPTIMAL CONTROL FOR THE OSEEN EQUATIONS WITH STABILIZED FINITE ELEMENTS.

Braack, Malte and Tews, Benjamin (2012) LINEAR-QUADRATIC OPTIMAL CONTROL FOR THE OSEEN EQUATIONS WITH STABILIZED FINITE ELEMENTS. Esaim-Control Optimisation and Calculus of Variations, 18 (4). pp. 987-1004.

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Abstract

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.

Document Type: Article
Research affiliation: Kiel University
OceanRep > The Future Ocean - Cluster of Excellence > FO-R09
OceanRep > The Future Ocean - Cluster of Excellence > FO-R11
OceanRep > The Future Ocean - Cluster of Excellence
Refereed: Yes
ISSN: 1292-8119
Projects: Future Ocean
Date Deposited: 14 May 2014 10:20
Last Modified: 08 Mar 2017 09:34
URI: http://oceanrep.geomar.de/id/eprint/23868

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