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Volume 5, Number 3, 2015, Pages 313-328                                                                DOI:10.11948/2015028
A global superconvergent $L^{\infty}$-error estimate of mixed finite element methods for semilinear elliptic optimal control problems
Li Li
Keywords:Semilinear elliptic equations;optimal control problems;superconvergence;mixed finite element methods
      In this paper, we discuss the superconvergence of mixed finite element methods for a semilinear elliptic control problem with an integral constraint. The state and costate are approximated by the order $k=1$ Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. Approximation of the optimal control of the continuous optimal control problem will be constructed by a projection of the discrete adjoint state. It is proved that this approximation has convergence order $h^{2}$ in $L^{\infty}$-norm. Finally, a numerical example is given to demonstrate the theoretical results.
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