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Main Title: PDE-constrained control using FEMLAB - Control of the Navier-Stokes equations
Author(s): Slawig, Thomas
Type: Research Paper
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.
Subject(s): optimal control
finite element method
Navier-Stokes equations
Comsol Multiphysics
PDE-constrained control
Issue Date: 30-Sep-2005
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
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
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2005, 26
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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