# ERROR ESTIMATES OF RT1 MIXED METHODS FOR DISTRIBUTED OPTIMAL CONTROL PROBLEMS

• Hou, Tianliang (Key Laboratory for Nonlinear Science and System Structure School of Mathematics and Statistics Chongqing Three Gorges University)
• Received : 2012.12.24
• Published : 2014.01.31

#### 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.

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