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

Malte Braack, Benjamin Tews (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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...

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