Superconvergence Of Finite Method For Optimal Control Problems Governed By Parabolic Equations

Optimal control problems are very important to many engineering applications. For the last decades, it has become a very active and successful research area. It is obvious that efficient numerical methods are very essential to successful solving the optimal control problems. Finite element approximation method plays an very important role in solving the optimal control problems.In this paper, we will investigate the superconvergence for the finite element approximation of quadratic optimal control problem governed by linear parabolic equation. The state and co-state are approximated by the piecewise linear functions and the control is approximated by piecewise constant functions. We will construct the approximation schemes for the model optimal control problem, then we will introduce some intermediate and get its error estimates, by using the results, we present the superconvergence analysis for both the control variables and the state variables.