Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations (Advances in Applied Mathematics and Mechanics, 2021)
In this paper, we investigate the error estimates of mixed finite elementmethods for optimal control problems governed by general elliptic equations. Thestate and co-state are approximated by the lowest order Raviart-Thomas mixed finiteelement 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 statevariables. Finally, a numerical example is given to demonstrate the theoretical results.