Brezzi-Pitkaranta stabilization and a priori error analysis for theStokes control

Abstract

In this study, we consider a Brezzi-Pitkaranta stabilization scheme for theoptimal control problem governed by stationary Stokes equation, using a P1-P1 interpolation for velocity and pressure. We express the stabilization asextra terms added to the discrete variational form of the problem. We firstprove the stability of the finite element discretization of the problem. Then, wederive a priori error bounds for each variable and present a numerical exampleto show the effectiveness of the stabilization clearly