(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
In this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L^2 and H^-1-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.