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Analysis and finite element error estimates for the velocitytracking problem for Stokes flows via a penalized formulation

Published online by Cambridge University Press:  15 October 2004

Konstantinos Chrysafinos
Konstantinos Chrysafinos*
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA 15213, USA; kchrysaf@zxc2.math.cmu.edu.
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Abstract

A distributed optimal control problem for evolutionary Stokes flows is studied via a pseudocompressibility formulation. Several results concerning the analysis of the velocity tracking problem are presented. Semidiscrete finite element error estimates for the corresponding optimality system are derived based on estimates for the penalized Stokes problem and the BRR (Brezzi-Rappaz-Raviart) theory. Finally, the convergence of the solutions of the penalized optimality systems as ε → 0 is examined.

Keywords

Optimal controlvelocity trackingfinite elementssemidiscrete error estimatesStokes equationspenalized formulation.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 4 , October 2004 , pp. 574 - 592
Copyright
© EDP Sciences, SMAI, 2004

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