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JIMO

In this paper, we investigate the superconvergence property of a
quadratic elliptic control problem with pointwise control
constraints. The state and the co-state variables are approximated
by the Raviart-Thomas mixed finite element of order
$k=1$ and the control variable is discretized by piecewise linear
but discontinuous functions. Approximations of the optimal solution
of the continuous optimal control problem will be constructed by a
projection of the discrete adjoint state. It is proved that these
approximations have convergence order $h^{2}$.

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