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

文献类型：期刊论文

作者Liu, Huaqing; Zhang, Linbo; Zhang, Xiaodi; Zheng, Weiying1
刊名COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
出版日期2020-08-01
卷号367页码:16
关键词Interface problem Unfitted mesh Interface-penalty finite element method Maxwell's equation Nitsche's method
ISSN号0045-7825
DOI10.1016/j.cma.2020.113137
英文摘要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.
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
语种英语
WOS记录号WOS:000564001800005
出版者ELSEVIER SCIENCE SA
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/52052]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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