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
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.
Email: email@example.com (Z. Lu), firstname.lastname@example.org (Y. Chen)