In this paper,we investigate the superconvergence property of the numerical solution to a quadratic elliptic control problem by using mixed finite element methods.The state and co-state are approximated by the order k...In this paper,we investigate the superconvergence property of the numerical solution to a quadratic elliptic control problem by using mixed finite element methods.The state and co-state are approximated by the order k=1 Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions.We prove the superconvergence error estimate of h3/2 in L2-norm between the approximated solution and the average L2 projection of the control.Moreover,by the postprocessing technique,a quadratic superconvergence result of the control is derived.展开更多
基金supported by National Natural Science Foundation of China(Grant No.10971074)Foundation for Talent Introduction of Guangdong Provincial University,Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20114407110009)
文摘In this paper,we investigate the superconvergence property of the numerical solution to a quadratic elliptic control problem by using mixed finite element methods.The state and co-state are approximated by the order k=1 Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions.We prove the superconvergence error estimate of h3/2 in L2-norm between the approximated solution and the average L2 projection of the control.Moreover,by the postprocessing technique,a quadratic superconvergence result of the control is derived.
