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
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65K10 Optimization and variational techniques
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65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
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35Q30 Stokes and Navier-Stokes equations
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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