| Abstract: | 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 $L^infty$-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. |
