Mixed finite element methods for identification distributed parameters

We study a priori error estimates of mixed finite element methods for identification distributed parameters. 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. Then, we construct the mixed finite element discretization for the identification distributed parameters. Furthermore, we derive a priori error estimates for the coupled state and control approximation. Finally, we present a numerical example which confirm our theoretical results.