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.
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