A priori error estimate and superconvergence analysis for an optimal control problem of bilinear type

In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal L-2-norm error estimates and the almost optimal L-infinity-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.