Abstract: | In this paper, we will investigate the error estimates and the
superconvergence property of mixed finite element methods for a
semilinear elliptic control problem with an integral constraint on
control. The state and co-state are approximated by the lowest order
Raviart-Thomas mixed finite element and the control variable
is approximated by piecewise constant functions. We derive some
superconvergence properties for the control variable and the state
variables. Moreover, we derive $L^∞$- 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. |