Analysis and Finite-Element Approximation of Optimal-Control Problems for the Stationary Navier-Stokes Equations with Distributed and Neumann Controls

Authors

Max D. GunzburgerFollow
L. HouFollow
Tom Svobodny, Wright State University - Main CampusFollow

Document Type

Article

Publication Date

7-1991

Abstract

We examine certain analytic and numerical aspects of optimal control problems for the stationary Navier-Stokes equations. The controls considered may be of either the distributed or Neumann type; the functionals minimized are either the viscous dissipation or the L⁴-distance of candidate flows to some desired flow. We show the existence of optimal solutions and justify the use of Lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced. We study the regularity of solutions of this system. Then, we consider the approximation, by finite element methods, of solutions of the optimality system and derive optimal error estimates.

Comments

First published in Mathematics of Computation 57.195 (1991), published by the American Mathematical Society.

Repository Citation

Gunzburger, M. D., Hou, L., & Svobodny, T. (1991). Analysis and Finite-Element Approximation of Optimal-Control Problems for the Stationary Navier-Stokes Equations with Distributed and Neumann Controls. Third International Conference on Mathematical and Numerical Aspects of Wave Propagation, 57 (195), 123-151.
https://corescholar.libraries.wright.edu/math/37

DOI

10.2307/2938666