Zuliang lu - School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing ۴۰۴۰۰۰,P.R.China;College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan ۴۱۱۱۰۵, P.R.China

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state areapproximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state and the control variable. As a result, it can be provedthat the discrete solutions possess the convergence property of order h . Finally, a numerical example is presented which confirms the theoretical results.

Priori error estimates, Parabolic optimal control, Integral constraint, Mixed finite element method, Variational discretization