A space-time multigrid solver for distributed control of the time-dependent Navier-Stokes system

We present a space-time hierarchical solution concept for optimization problems governed by the time-dependent Navier–Stokes system. Discretisation is carried out with finite elements in space and a one-step-θ-scheme in time. By combining a Newton solver for the treatment of the nonlinearity with a space-time multigrid solver for linear subproblems, we obtain a robust solver whose convergence behaviour is independent of the number of unknowns of the discrete problem and robust with regard to the considered flow configuration. A set of numerical examples analyses the solver behaviour for various problem settings with respect to the efficiency of this approach.

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