Error estimates of RT1 mixed methods for distributed optimal control problems
Bull. Korean Math. Soc. 2014 Vol. 51, No. 1, 139-156
Printed January 1, 2014
Tianliang Hou
Chongqing Three Gorges University
Abstract : In this paper, we investigate the error estimates of a quadratic elliptic control problem with pointwise control constraints. The state and the co-state variables are approximated by the order $k=1$ Raviart-Thomas mixed finite element and the control variable is discretized by piecewise linear but discontinuous functions. Approximations of order $h^{\frac{3}{2}}$ in the $L^{2}$-norm and order $h$ in the $L^{\infty}$-norm for the control variable are proved.
Keywords : elliptic equations, distributed optimal control problems, $L^{\infty}$-error estimates, RT1 mixed finite element methods
MSC numbers : 49J20, 65N30
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