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Variational discretization and rectangle mixed finite element methods for quadratic semilinear elliptic optimal control problems

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1 Author(s)
Zuliang Lu ; Sch. of Math. & Stat., Chongqing Three Gorges Univ., Chongqing, China

In this paper, we investigate a variational discretization and rectangle mixed finite element methods for the quadratic optimal control problems governed by semilinear elliptic equations. The state and the co-state are approximated by the lowest order Raviart-Thomas rectangle mixed finite element spaces and the control is not discretized. Optimal error estimates are established for the state and control variable. As a result, it can be proved that the discrete solutions possess the convergence property of order h. A numerical example is presented to confirm our theoretical results.

Published in:

Electrical Engineering Computing Science and Automatic Control (CCE), 2011 8th International Conference on

Date of Conference:

26-28 Oct. 2011