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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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