Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with distributed and Neumann controls

Authors:
M. D. Gunzburger, L. Hou and T. P. Svobodny

Journal:
Math. Comp. **57** (1991), 123-151

MSC:
Primary 65K10; Secondary 35B37, 35Q30, 49M25, 65N30, 76D05, 76M10

DOI:
https://doi.org/10.1090/S0025-5718-1991-1079020-5

MathSciNet review:
1079020

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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 -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.

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DOI:
https://doi.org/10.1090/S0025-5718-1991-1079020-5

Article copyright:
© Copyright 1991
American Mathematical Society