Adv. Appl. Math. Mech., 1 (2009), pp. 242-256. 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, 65N30 Key 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)