A characteristic-mixed finite element method for time-dependent convection–diffusion optimal control problem

In this paper, we examine the method of characteristic-mixed finite element for the approximation of convex optimal control problem governed by time-dependent convection–diffusion equations with control constraints. For the discretization of the state equation, the characteristic finite element is used for the approximation of the material derivative term (i.e., the time derivative term plus the convection term), and the lowest-order Raviart–Thomas mixed element is applied for the approximation of the diffusion term. We derive some a priori error estimates for both the state and control approximations.