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

Author： Chrysafinos Konstantinos  

Publisher： Edp Sciences

E-ISSN： 1262-3377|10|4|574-592

ISSN： 1292-8119

Source： ESAIM: Control, Optimisation and Calculus of Variations, Vol.10, Iss.4, 2010-03, pp. : 574-592

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

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

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