Error estimates of variational discretization and mixed finite element methods for quasilinear optimal control problems

In this paper we study a variational discretization and mixed finite element approximation of optimal control problems governed by quasilinear elliptic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. We derive a priori error estimates both for the state variables and the control variable. Finally, a numerical example is given to demonstrate the theoretical results.