Superconvergence for Optimal Control Problems Governed by Semi-linear Elliptic Equations

Authors:
Yanping Chen;Yongquan Dai
Affiliations:
School of Mathematical Sciences, South China Normal University, Guangzhou, People's Republic of China 510631;Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics, Xiangtan University, Xiangtan, People's Republic of China 411105
Venue:
Journal of Scientific Computing
Year:
2009

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Abstract

In this paper, we will investigate the superconvergence of the finite element approximation for quadratic optimal control problem governed by semi-linear elliptic equations. The state and co-state variables are approximated by the piecewise linear functions and the control variable is approximated by the piecewise constant functions. We derive the superconvergence properties for both the control variable and the state variables. Finally, some numerical examples are given to demonstrate the theoretical results.