Numerical approximation of a class of nonlinear parabolic optimal control problems

In the paper we mainly consider the finite element numerical solutions for a class of optimal control problem governed by nonlinear parabolic equations. We derive an error estimates for the coupled state and the control solutions of the nonlinear parabolic optimal control problems. The state and co-state are approximated by the mixed finite element spaces and the control is approximated by piecewise constant functions. Finally, we give a numerical example to show the theoretical results.