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

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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.

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Authors and Affiliations

  1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics, Xiangtan University, Xiangtan, 411105, People’s Republic of China

    Yongquan Dai

  2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, Guangdong, People’s Republic of China

    Yanping Chen

Authors
  1. Yanping Chen
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  2. Yongquan Dai
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Corresponding author

Correspondence to Yanping Chen.

Additional information

This work is supported by National Science Foundation of China, the National Basic Research Program under the Grant 2005CB321703, Scientific Research Fund of Hunan Provincial Education Department, and Hunan Provincial Innovation Foundation for Postgraduate (No. S2008yjscx04).

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Chen, Y., Dai, Y. Superconvergence for Optimal Control Problems Governed by Semi-linear Elliptic Equations. J Sci Comput 39, 206–221 (2009). https://doi.org/10.1007/s10915-008-9258-9

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  • DOI: https://doi.org/10.1007/s10915-008-9258-9

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