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Research articles

ScienceAsia 42 (2016): 213-221 |doi: 10.2306/scienceasia1513-1874.2016.42.213

Superconvergence of triangular mixed finite element methods for nonlinear optimal control problems

Zuliang Lua,*, Shuhua Zhangb

ABSTRACT:     In this paper, we investigate the superconvergence of nonlinear elliptic optimal control problems by using triangular mixed finite element methods. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We obtain the superconvergence of O(h3/2) for the control variable and coupled state variable. Numerical results demonstrating these superconvergence results are also presented.

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a Key Laboratory for Nonlinear Science and System Structure, Key Laboratory of Signal and Information Processing, Chongqing Three Gorges University, Chongqing 404000, China
b Research Centre for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin 300222, China

* Corresponding author, E-mail: zulianglux@126.com

Received 9 Apr 2015, Accepted 0 0000