A PENALIZED NEUMANN CONTROL APPROACH FOR SOLVING AN OPTIMAL DIRICHLETCONTROL PROBLEM FOR THE NAVIER-STOKES EQUATIONS

We introduce a penalized Neumann boundary control approach for solving an optimal Dirichlet boundary control problem associated with the two - or three-dimensional steady-state Navier-Stokes equations. We prove the convergence of the solutions of the penalized Neumann control prob lem, the suboptimality of the limit, and the optimality of the limit u nder further restrictions on the data. We describe the numerical algor ithm for solving the penalized Neumann control problem and report some numerical results.