摘要
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.
基金
supported in part by Hunan Education Department Key Project 10A117 and Hunan Provincial Innovation Foundation for Postgraduate CX2010B247
supported by the Foundation for Talent Introduction of Guangdong Provincial University,Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008)and National Science Foundation of China(10971074)
supported in part by the NSFC Key Project(11031006)
Hunan Provincial NSF Project(10JJ7001)
the NSFC for Distinguished Young Scholars(10625106)
National Basic Research Program of China under the Grant 2005 CB321701.
