Error analysis of finite element approximations of the optimal control problem for stochastic Stokes equations with additive white noise

Finite element approximation solutions of the optimal control problems for stochastic Stokes equations with the forcing term perturbed by white noise are considered. To obtain the most efficient deterministic optimal control, we set up the cost functional as we proposed in [20]. Error estimates are established for the fully coupled optimality system using Green's functions and Brezzi-Rappaz-Raviart theory. Numerical examples are also presented to examine our theoretical results.