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Constrained Optimal Control of Navier-Stokes Flow by Semismooth Newton Methods

Michael Ulbrich

Technische Universität München

Zentrum Mathematik

Lehrstuhl für Angewandte Mathematik und Mathematische Statistik

Technical Report

September 2001

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We propose and analyze a semismooth Newton-type method for the solution of a pointwise constrained optimal control problem governed by the time-dependent incompressible Navier-Stokes equations. The method is based on a reformulation of the optimality system as an equivalent nonsmooth operator equation. We analyze the flow control problem and establish q-superlinear convergence of the method. In the numerical implementation, adjoint techniques are combined with a truncated conjugate gradient method. Numerical results are presented that support our theoretical results and confirm the viability of the approach.