Superconvergence for elliptic optimal control problems discretized by RT1 mixed finite elements and linear discontinuous elements
Tianliang Hou Yanping Chen
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 $h^{2}$.
keywords: postprocessing. discontinuous functions mixed finite element methods Elliptic equations optimal control problems superconvergence

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