Global superconvergence for optimal control problems governed by Stokes equations

In this paper, the global superconvergence analysis for the finite element approximation of the distributed optimal control governed by Stokes equations is discussed. For the control, a global superconvergence result is derived by applying patch recovery technique. For the state and the co-state, the global superconvergence results are derived by applying some postprocessing techniques for the bilinear-constant scheme over the uniform rectangular meshes. Based on the global superconvergence analysis, recovery type a posteriori error estimates are derived. It is shown that the recovery type a posteriori error estimators provided in this paper are asymptotically exact if the conditions for the superconvergence are satisfied.