A posteriori error estimates for a distributed optimal control problem of the stationary Navier-Stokes equations

In two and three dimensional Lipschitz, but not necessarily convex, polytopal domains, we propose and analyze an a posteriori error estimator for an optimal control problem that involves the stationary Navier-Stokes equations; control constraints are also considered. The proposed error estimator is defined as the sum of three contributions, which are related to the discretization of the state and adjoint equations and the control variable. We prove that the devised error estimator is globally reliable and locally efficient. We conclude by presenting numerical experiments which reveal the competitive performance of an adaptive loop based on the proposed error estimator.