Nonconforming immersed finite element method for solving elliptic optimal control problems with interfaces. Issue 6 (13th April 2022)

• Record Type: Journal Article
• Authors: Wang, Quanxiang; Xie, Jianqiang; Zhang, Zhiyue
• Is Part Of: Applicable analysis. Volume 101:Issue 6(2022)
• Page Start: 2197
• Page End: 2216
• Publication Date: 2022-04-13
• Subjects: R. Magnanini; Nonconforming -- immersed finite element -- interface -- optimal control; 65M99 -- 82B24 -- 49M05 -- 65K10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1802431
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we present a nonconforming immersed finite element method for solving elliptic optimal control problems with interfaces. The immersed finite element space is constructed based on the rotated-Q1 nonconforming finite elements with the integral-value degrees of freedom. The method can overcome the difficulties encountered by conforming immersed finite element method. We derive error estimates for the control, state and adjoint state in both energy and L 2 norms. Numerical results are reported to support the theoretical analysis.