Two-grid methods of mixed covolume approximations for elliptic optimal control problems

Abstract In this paper, we focus on the mixed covolume approximation for a class of linear elliptic optimal control problems, and devise a two-grid algorithm. The state and costate are approximated using the lowest-order Raviart–Thomas mixed finite elements, while the control is discretized by means of piecewise constant functions. First, the mixed covolume approximation of the optimal control problems is constructed via the discretize-then-optimize approach. Second, the a priori error estimates for the state variables, costate variables and the control variable are established. Finally, a two-grid algorithm is formulated, and its convergence is analysed.