Parameter‐robust preconditioning for unsteady Stokes control problems

We propose a saddle-point preconditioner for an optimization problem constrained by the time-dependent Stokes equations, discretized using backward Euler method in time. The key ingredients are inner iteration (1, 1)-block, accelerated known heat control problem, and approximation of Schur complement involving commutator argument applied to block matrix. Numerical results demonstrate efficacy robustness this approach.