Nonconforming immersed finite element method for solving elliptic optimal control problems with interfaces

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.

COMMUNICATED BY:

• R. Magnanini

Keywords:

• Nonconforming
• immersed finite element
• interface
• optimal control

2010 Mathematics Subject Classifications:

• 65M99
• 82B24
• 49M05
• 65K10

Acknowledgments

This project is partially supported by the National Natural Science Foundation of China Nos. 11701283, 11971241, the Fundamental Research Funds for the Central Universities No. KJQN201839, and Excellent Young Talents Science and Technology Fund of College of Engineering No. YQ 201607.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This project is partially supported by the National Natural Science Foundation of China [grant numbers 11701283, 11971241], the Fundamental Research Funds for the Central Universities [grant number KJQN201839], and Excellent Young Talents Science and Technology Fund of College of Engineering [grant number YQ 201607].