# Linear-quadratic optimal control for the Oseen equations with stabilized finite elements

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 4, page 987-1004
- ISSN: 1292-8119

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topBraack, Malte, and Tews, Benjamin. "Linear-quadratic optimal control for the Oseen equations with stabilized finite elements." ESAIM: Control, Optimisation and Calculus of Variations 18.4 (2012): 987-1004. <http://eudml.org/doc/272857>.

@article{Braack2012,

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.},

author = {Braack, Malte, Tews, Benjamin},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Oseen; Navier-Stokes; optimal control; finite elements; stabilized methods; quadratic cost functional; discretize-optimize; optimize-discretize; boundary layers},

language = {eng},

number = {4},

pages = {987-1004},

publisher = {EDP-Sciences},

title = {Linear-quadratic optimal control for the Oseen equations with stabilized finite elements},

url = {http://eudml.org/doc/272857},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Braack, Malte

AU - Tews, Benjamin

TI - Linear-quadratic optimal control for the Oseen equations with stabilized finite elements

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2012

PB - EDP-Sciences

VL - 18

IS - 4

SP - 987

EP - 1004

AB - 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.

LA - eng

KW - Oseen; Navier-Stokes; optimal control; finite elements; stabilized methods; quadratic cost functional; discretize-optimize; optimize-discretize; boundary layers

UR - http://eudml.org/doc/272857

ER -

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