Abstract: An a posteriori error analysis is obtained for mixed finite element approximation of quadratic convex optimal control problem governed by nonlinear elliptic equation.The state and the co-state are approximated by the k-th R-T mixed finite element spaces and the control is approximated by piecewise constant functions.The results are based on the approximation for both the state variables and the control variable.In numerical experiments,the posteriori error estimators are used as the mesh refinement indicator.Then it is clear that the adaptive finite element method is more efficient.

Key words: nonlinear optimal control, mixed finite element approximation, posteriori error estimates