A Priori Error Estimate and Superconvergence Analysis for an Optimal Control Problem of Bilinear Type (Journal of Computational Mathematics, 2018)
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 $L^∞$-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.
Keywords: Bilinear control problem; Finite element approximation; Superconvergence; A priori error estimate; A posteriori error estimator.