A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations
Tianliang Hou 1, Yanping Chen 2*, Yunqing Huang 11 Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics, Xiangtan University, Xiangtan 411105, Hunan, China.
2 School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, China.
Received 8 July 2010; Accepted (in revised version) 25 December 2010
In this paper, we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.AMS subject classifications: 49J20, 65N30
Key words: A posteriori error estimates, quadratic optimal control problems, parabolic equations, mixed finite element methods.
Email: firstname.lastname@example.org (T. Hou), email@example.com (Y. Chen), firstname.lastname@example.org (Y. Huang)