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PDE-constrained control using Femlab – Control of the Navier–Stokes equations

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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.

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  1. TU Berlin, Institut f. Mathematik, Strasse des 17. Juni 136 MA 4–5, 10623, Berlin, Germany

    Thomas Slawig

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  1. Thomas Slawig
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Correspondence to Thomas Slawig.

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Communicated by Claude Brezinski.

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Slawig, T. PDE-constrained control using Femlab – Control of the Navier–Stokes equations. Numer Algor 42, 107–126 (2006). https://doi.org/10.1007/s11075-006-9026-6

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  • DOI: https://doi.org/10.1007/s11075-006-9026-6

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