The local discontinuous Galerkin method for optimal control problem governed by convection-diffusion equations

Abstract. In this paper we analyze the Local Discontinuous Galerkin (LDG) method for the constrained optimal control problem governed by the unsteady convection diffusion equations. A priori error estimates are obtained for both the state, the adjoint state and the control. For the discretization of the control we discuss two different approaches which have been used for elliptic optimal control problem. Key Words. Local Discontinuous Galerkin method, unsteady convection dif-fusion equations, constrained optimal control problem, a priori error estimate. 1