Variational multiscale method for the optimal control problems ofconvection{diffusion{reaction equations

Abstract

In this paper, we analyze a projection-based variational multiscale (VMS) method for the optimal controlproblems governed by the convection{diffusion{reaction equations. We derive the rst-order optimality conditions by theoptimize-then-discretizemethod. After expressing the discrete optimal control problem, we obtain the stability propertiesof state and adjoint variables. We also prove that the error in each variable is optimal. Through numerical examples,we show the efficiency of the stabilization for the solutions of the control, state, and adjoint variables