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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 Publication COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING ISSN 0045-7825 Volume 367Pages:16 Abstract 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. Keyword Interface problem Unfitted mesh Interface-penalty finite element method Maxwell's equation Nitsche's method DOI 10.1016/j.cma.2020.113137 Indexed By SCI Language 英语 Funding Project 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 Research Area Engineering ; Mathematics ; Mechanics WOS Subject Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics WOS ID WOS:000564001800005 Publisher ELSEVIER SCIENCE SA Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/52053 Collection 计算数学与科学工程计算研究所 Corresponding Author Zheng, Weiying Affiliation 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS,LSEC, Beijing 100190, Peoples R China2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China Recommended CitationGB/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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