A finite element method for elliptic optimal control problem on a non-convex polygon with corner singularities. (1st January 2018)

• Record Type: Journal Article
• Authors: Choi, Hyung Jun; Choi, Woocheol; Koh, Youngwoo
• Is Part Of: Computers & mathematics with applications. Volume 75:issue 1(2018)
• Page Start: 45
• Page End: 58
• Publication Date: 2018-01-01
• Subjects: Elliptic optimal control problem -- Corner singularity -- Non-convex polygon; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.08.029
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we study a finite element method overcoming corner singularities for elliptic optimal control problem posed on a polygon. Based on a corner singularity decomposition of singular solution for the associated elliptic system, we derive an extraction formula for coefficients of singular parts, called stress intensity factors, and introduce a finite element discretization for regular parts of the solution pair. Furthermore, we analyze the finite element solutions in L 2 and H 1 norms. By numerical experiments, we confirm the efficiency and reliability of the proposed method.