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Adv. Appl. Math. Mech., 1 (2009), pp. 242-256. |
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A Posteriori Error Estimates of Triangular Mixed Finite Element Methods for Semilinear Optimal Control Problems Zuliang Lu 1, Yanping Chen 2* 1 Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics, Xiangtan University, Xiangtan 411105, Hunan, P.R.China.2 School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, P.R.China. Received 31 October 2008; Accepted (in revised version) 24 December 2008 Abstract In this paper, we present an a posteriori error estimates of semilinear quadratic constrained optimal control problems using triangular mixed finite element methods. The state and co-state are approximated by the order $k\leq 1$ Raviart- Thomas mixed finite element spaces and the control is approximated by piecewise constant element. We derive a posteriori error estimates for the coupled state and control approximations. A numerical example is presented in confirmation of the theory. AMS subject classifications: 49J20, 65N30Key words: Semilinear optimal control problems; mixed finite element methods; a posteriori error estimates. *Corresponding author. Email: zulianglux@126.com (Z. Lu), yanpingchen@scnu.edu.cn (Y. Chen) |