Error estimates of mixed finite element methods for quadratic optimal control problems

In this paper, we investigate the error estimates for the solutions of optimal control problems by mixed finite element methods. The state and costate are approximated by Raviart–Thomas mixed finite element spaces of order kk and the control is approximated by piecewise polynomials of order kk. Under the special constraint set, we will show that the control variable can be smooth in the whole domain. We derive error estimates of optimal order both for the state variables and the control variable.