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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
Source PublicationCOMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
ISSN0045-7825
Volume367Pages:16
AbstractIn 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.
KeywordInterface problem Unfitted mesh Interface-penalty finite element method Maxwell's equation Nitsche's method
DOI10.1016/j.cma.2020.113137
Indexed BySCI
Language英语
Funding ProjectNational 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 Research AreaEngineering ; Mathematics ; Mechanics
WOS SubjectEngineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
WOS IDWOS:000564001800005
PublisherELSEVIER SCIENCE SA
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/52053
Collection计算数学与科学工程计算研究所
Corresponding AuthorZheng, Weiying
Affiliation1.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
Recommended Citation
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.
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