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Preprint 26-2005

PDE-constrained control using FEMLAB - Control of the Navier-Stokes equations

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Author(s) : Thomas Slawig

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 26-2005

MSC 2000

49K20 Problems involving partial differential equations
65K10 Optimization and variational techniques
65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
35Q30 Stokes and Navier-Stokes equations
76D05 Navier-Stokes equations

Abstract :
We show how the software FEMLAB can be used to solve PDE-constrained optimal control problems. We give a general formulation for such kind of problems and derive the adjoint equation and optimality system. Then these preliminaries are specified for the stationary Navier-Stokes equations with distributed and boundary control. The main steps to define and solve a PDE with FEMLAB are described. We describe how the adjoint system can be implemented, and how the optimality system can be used by FEMLAB's built-in functions. Special crucial topics concerning efficiency are discussed. Examples with distributed and boundary control for different type of cost functionals in 2 and 3 space dimensions are presented.

Keywords : Optimal control, finite element method, Navier-Stokes equations

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