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http://dx.doi.org/10.4134/BKMS.2014.51.1.139

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.1, 2014 , pp. 139-156 More about this Journal
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;
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