A priori and a posteriori error estimates of H1-Galerkin mixed finite element methods for elliptic optimal control problems. (November 2015)

• Record Type: Journal Article
• Authors: Hou, Tianliang
• Is Part Of: Computers & mathematics with applications. Volume 70:issue 10(2015)
• Page Start: 2542
• Page End: 2554
• Publication Date: 2015-11
• Subjects: Elliptic equations -- Optimal control problems -- A priori error estimates -- A posteriori error estimates -- H1-Galerkin mixed finite element methods; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2015.09.018
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we investigate numerical approximations of H 1 -Galerkin mixed finite element methods for elliptic optimal control problems. The presented scheme is independent symmetric and positive definite for the state variables and the adjoint state variables. Moreover, the matching relation (i.e., LBB-condition) between the mixed element spaces V h and W h is not necessary, thus, we can choose the approximation spaces more flexibly. The state and co-state are approximated by the lowest order Raviart–Thomas mixed finite element spaces and the standard finite element spaces, the control variable is approximated by piecewise constant functions. We derive a priori and a posteriori error estimates for the control variable, the state variables and the adjoint state variables. Finally, some numerical examples are given to demonstrate the theoretical results about a priori error estimates.