Virginia TechGunzburger, Max D.Manservisi, S.2014-05-282014-05-282000-05Gunzburger, M. D.; Manservisi, S., "Analysis and approximation of the velocity tracking problem for Navier-Stokes flows with distributed control," SIAM J. Numer. Anal., 37(5), 1481-1512, (2000). DOI: 10.1137/s00361429973294140036-1429http://hdl.handle.net/10919/48149We consider the mathematical formulation, analysis, and the numerical solution of a time-dependent optimal control problem associated with the tracking of the velocity of a Navier-Stokes ow in a bounded two-dimensional domain through the adjustment of a distributed control. The existence of optimal solutions is proved and the first-order necessary conditions for optimality are used to derive an optimality system of partial differential equations whose solutions provide optimal states and controls. Semidiscrete-in-time and fully discrete space-time approximations are defined and their convergence to the exact optimal solutions is shown. A gradient method for the solution of the fully discrete equations is examined, as are its convergence properties. Finally, the results of some illustrative computational experiments are presented.en-USIn Copyrightoptimal controlnavier-stokes equationsfinite elementsfluidmechanicsfinite-element approximationequationsdynamicsmathematics, appliedArticle - Refereedhttp://epubs.siam.org/doi/abs/10.1137/S0036142997329414https://doi.org/10.1137/s0036142997329414