Volume 7, Number 3, 2017, Pages 10371050 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. 
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 costate are approximated by the order $k=1$ RaviartThomas 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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