A priori error estimates of mixed methods for bilinear elliptic optimal control problems with integral constraint

We study a priori error estimates of mixed finite element methods for optimal control problem governed by bilinear elliptic equations with integral constraint. The state and the co-state are discretized by the lowest order Raviart-Thomas mixed finite element spaces and the control is discretized by piecewise constant elements. We derive a priori error estimates for the coupled state and control approximation. Finally, we present an numerical example which confirm our theoretical results.