New numerical method for solving optimal control problem for the stationary Navier-Stokes equations

The purpose of this article is to propose a new numerical method to solve the problem of optimal control of the steady-state Navier-Stokes equations via the velocity-pressure formulation. We apply a new technique to derive a system of equations from which the solution can be calculated. The spectral method is used to discretize the problem. An extended relaxation method is proposed in the numerical part to ensure the correct convergence of the system. Finally, numerical results are provided to confirm the effectiveness of this approach.