Upwind approximations and mesh independence for LQR control of convection diffusion equations

The development of practical computational schemes for optimization and control of non-normal distributed parameter systems requires that one builds certain computational efficiencies (such as mesh independence) into the approximation scheme. We consider some numerical issues concerning the application of Kleinman-Newton algorithms to discretizations of infinite dimensional Riccati equations that arise in control of PDE systems. We show that dual convergence and compactness play central roles in both convergence and mesh independence and we present numerical results to illustrate the theory.