(untitled) (Journal of Computational Mathematics, 2018)
In this paper, a full discrete local projection stabilized (LPS) method is proposed to solve the optimal control problems of the unsteady Navier-Stokes equations with equal order elements. Convective effects and pressure are both stabilized by using the LPS method. A priori error estimates uniformly with respect to the Reynolds number are obtained, providing the true solutions are sufficiently smooth. Numerical experiments are implemented to illustrate and confirm our theoretical analysis.