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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with distributed and Neumann controls
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by M. D. Gunzburger, L. Hou and T. P. Svobodny PDF
Math. Comp. 57 (1991), 123-151 Request permission

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 ${{\mathbf {L}}^4}$-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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Additional Information
  • © Copyright 1991 American Mathematical Society
  • 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