===affil2: UMBC ===firstname: Andrei ===firstname4: ===firstname3: ===lastname2: Soane ===lastname: Draganescu ===firstname5: ===affil6: ===lastname3: ===email: draga@umbc.edu ===lastname6: ===affil5: ===otherauths: ===lastname4: ===affil4: ===lastname7: ===affil7: ===firstname7: ===postal: Department of Mathematics and Statistics UMBC 1000 Hilltop Circle Baltimore, MD 21250 ===firstname6: ===ABSTRACT: We construct multigrid preconditioners to accelerate the solution process of optimal control problems constrained by the Stokes/Navier-Stokes equations. Our approach for the Stokes control problem is to eliminate the state and adjoint variables from the optimality system and to construct efficient multigrid preconditioners for the Schur-complement of the block associated with these variables. Similar preconditioners are constructed for the reduced Hessian in the Newton-PCG method for the optimal control of the stationary Navier-Stokes equations. ===affil3: ===lastname5: ===affilother: ===title: Multigrid Preconditioners for Optimal Control Problems in Fluid Flow ===firstname2: Ana Maria