Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity (Advances in Applied Mathematics and Mechanics, 2021)
In this paper, we investigate the error estimates andsuperconvergence property of mixed finite element methods forelliptic optimal control problems. The state and co-state areapproximated by the lowest order Raviart-Thomas mixed finite elementspaces and the control variable is approximated by piecewiseconstant functions. We derive $L^2$ and $L^∞$-errorestimates for the control variable. Moreover, using a recoveryoperator, we also derive some superconvergence results for thecontrol variable. Finally, a numerical example is given todemonstrate the theoretical results.