Analysis and finite element approximation of some optimal control problems associated with the NavierStokes equations
Abstract
The finite element approximation of several optimal control problems associated with the stationary NavierStokes equations is studied. The controls may be the distributed type (external body force), Dirichlet type (velocity on the boundary), Neumann type (stress on the boundary), or a combination of these. The optimization goal is either to minimize the viscous drag or to obtain a best approximation in the L sup 4 (omega) sense to some desired flow field. For the various cases the existence of optimal solutions is proved, and using Lagrange multiplier techniques, an optimality system of equations is derived. The regularity of solutions of the optimality systems is studied. Finally, finite element algorithms are defined and optimal error estimates are obtained.
 Publication:

Ph.D. Thesis
 Pub Date:
 March 1989
 Bibcode:
 1989PhDT........38H
 Keywords:

 Algorithms;
 Dirichlet Problem;
 Finite Element Method;
 Flow Distribution;
 NavierStokes Equation;
 Optimal Control;
 Error Analysis;
 Lagrange Multipliers;
 Optimization;
 Viscous Drag;
 Fluid Mechanics and Heat Transfer