A priori error estimates for higher order variational discretization and mixed finite element methods of optimal control problems
1 College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, PR China
2 School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404000, PR China
3 School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China
4 Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics, Xiangtan University, Xiangtan 411105, Hunan, PR China
Journal of Inequalities and Applications 2012, 2012:95 doi:10.1186/1029-242X-2012-95Published: 20 April 2012
In this article, we investigate a priori error estimates for the optimal control problems governed by elliptic equations using higher order variational discretization and mixed finite element methods. The state and the co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control is not discreted. A priori error estimates for the higher order variational discretization and mixed finite element approximation of control problems are obtained. Finally, we present some numerical examples which confirm our theoretical results.
Mathematics Subject Classification 1991: 49J20; 65N30.