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In this work we construct multigrid preconditioners to be used in the Newton-Krylov method for a distributed optimal control problem constrained by the stationary Navier-Stokes equations. These preconditioners are shown to be of optimal order with respect to the convergence properties of the discrete methods use to solve the Navier-Stokes equations.doi:10.13016/m2bv79x58 fatcat:ph7c7i2hijgajknsrjrwzmhtly