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Volume 7, Number 3, 2017, Pages 1037-1050                                                                DOI:10.11948/2017065
A superconvergent $L^{\infty}$-error estimate of RT1 mixed methods for elliptic control problems with an integral constraint
Yuelong Tang and Yuchun Hua
Keywords:Elliptic equations, optimal control problems, superconvergence, mixed finite element methods, postprocessing.
      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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