| A superconvergent $L^infinity$-error estimate of rt1 mixed methods for elliptic control problems with an integral constraint |
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| 作者姓名： | Yuelong Tang Yuchun Hua |
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| 摘 要： |
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| 收稿时间： | 2016/9/30 0:00:00 |
| 修稿时间： | 2016/9/30 0:00:00 |
A superconvergent $L^{\infty}$-error estimate of RT1 mixed methods for elliptic control problems with an integral constraint |
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| Yuelong Tang,Yuchun Hua.A superconvergent $L^infinity$-error estimate of rt1 mixed methods for elliptic control problems with an integral constraint[J].Journal of Applied Analysis & Computation,2017,7(3):1037-1050. |
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| Authors: | Yuelong Tang and Yuchun Hua |
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| Institution: | College of Science, Hunan University of Science and Engineering, 425100 Yongzhou, China;School of Mathematical Sciences, Peking University, 100871 Beijing, China,College of Science, Hunan University of Science and Engineering, 425100 Yongzhou, China |
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| Abstract: | In this paper, we investigate the superconvergence property of mixed finite element methods for a linear elliptic control problem with an integral constraint. The state and co-state are approximated by the order $k=1$ Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. A superconvergent approximation of the control variable $u$ will be constructed by a projection of the discrete adjoint state. It is proved that this approximation have convergence order $h^{2}$ in $L^{\infty}$-norm. Finally, a numerical example is given to demonstrate the theoretical results. |
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| Keywords: | Elliptic equations optimal control problems superconvergence mixed finite element methods postprocessing |
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