Interface-penalty finite element methods for interface problems in H-1, H(curl), and H(div)

doi:10.1016/j.cma.2020.113137

	Interface-penalty finite element methods for interface problems in H-1, H(curl), and H(div)
	Liu, Huaqing ; Zhang, Linbo ; Zhang, Xiaodi ; Zheng, Weiying1
	2020-08-01
发表期刊	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
ISSN	0045-7825
卷号	367 页码:16
摘要	In this article, interface-penalty finite element methods are proposed to solve interface problems in H-1, H(curl), H(div) spaces on unfitted tetrahedral meshes. The transmission conditions across the interface are derived in a unified framework for three types of interface problems. Usually, the well-posedness of an H-1-elliptic problem requires two transmission conditions for both the solution and the normal flux. The well-posedness for H(curl)- or H(div)-elliptic problem requires three transmission conditions. This provides the guideline for designing stable high-order finite element methods on unfitted meshes. Optimal error estimates are proven in energy norms for interface-penalty finite element methods within a unified framework for H-1, H(curl), and H(div). All error estimates are independent of the location of the interface relative to the mesh. High-order numerical quadrature rules are employed to compute surface integrals and volume integrals in sub-domains with curved boundaries which are produced by the intersection of the interface and the tetrahedral mesh. Numerical examples show optimal convergence of the proposed finite element methods for piecewise smooth solutions. (C) 2020 Elsevier B.V. All rights reserved.
关键词	Interface problem Unfitted mesh Interface-penalty finite element method Maxwell's equation Nitsche's method
DOI	10.1016/j.cma.2020.113137
收录类别	SCI
语种	英语
资助项目	National Science Fund for Distinguished Young Scholars of China[11725106] ; National Key Research and Development Program of China[2016YFB0201304] ; China NSF[91430215] ; China NSF[91530323] ; China NSF[11831016]
WOS研究方向	Engineering ; Mathematics ; Mechanics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
WOS记录号	WOS:000564001800005
出版者	ELSEVIER SCIENCE SA
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52053
专题	计算数学与科学工程计算研究所
通讯作者	Zheng, Weiying
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS,LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Liu, Huaqing,Zhang, Linbo,Zhang, Xiaodi,et al. Interface-penalty finite element methods for interface problems in H-1, H(curl), and H(div)[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2020,367:16.
APA	Liu, Huaqing,Zhang, Linbo,Zhang, Xiaodi,&Zheng, Weiying.(2020).Interface-penalty finite element methods for interface problems in H-1, H(curl), and H(div).COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,367,16.
MLA	Liu, Huaqing,et al."Interface-penalty finite element methods for interface problems in H-1, H(curl), and H(div)".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 367(2020):16.