A posteriori error estimates of the lowest order Raviart-Thomas mixed finite element methods for convective diffusion optimal control problems

In this paper, we consider the mixed finite element methods for quadratic optimal control problems governed by convective diffusion equations. The state and the co-state are discretized by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. Using some proper duality problems, we derive a posteriori L-2(0, T; L-2(Omega)) error estimates for the scalar functions. Such estimates, which are apparently not available in the literature, are an important step toward developing reliable adaptive mixed finite element approximation schemes for the control problem.