Analysis and finite element error estimates for the velocity tracking problem for Stokes flows via a penalized formulation
Department of Mathematical Sciences, Carnegie Mellon
University, Pittsburgh PA 15213, USA; email@example.com.
Revised: 16 December 2003
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.
Mathematics Subject Classification: 35B37 / 65M60 / 49J20
Key words: Optimal control / velocity tracking / finite elements / semidiscrete error estimates / Stokes equations / penalized formulation.
© EDP Sciences, SMAI, 2004