A Fully Divergence-Free Finite Element Scheme for Stationary Inductionless Magnetohydrodynamic Equations

doi:10.1007/s10915-021-01708-4

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	A Fully Divergence-Free Finite Element Scheme for Stationary Inductionless Magnetohydrodynamic Equations
	Zhang, Xiaodi 1; Wang, Xiaorong 2,3
	2022-02-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	90 期号:2 页码:30
摘要	In this paper, we propose and analyze a mixed finite element scheme for stationary inductionless magnetohydrodynamic equations on a general Lipschitz domain. We adopt divergence-conforming elements for the velocity and the current density, discontinuous elements for the pressure and the electric potential, thus the approximations for velocity and current density are exactly divergence-free. The H-1-continuity of the velocity is enforced by discontinuous Galerkin approach. With this discretization, we prove the well-posedness of the discrete scheme, and derive optimal error estimates of the discrete solutions. In particular, we show that the error estimates for the velocity and the current density are independent of the pressure and the electric potential, and the error estimates for the pressure and the electric potential are also unrelated to each other. Based on this, we propose two coupled iterative methods: Stokes and Oseen iterations. Rigorous analysis of convergence and stability is provided. Finally, some numerical examples are performed to verify the theoretical results and show the effectiveness of the presented methods.
关键词	Mixed finite element method Divergence-free Inductionless MHD equations Conservation of charge and mass
DOI	10.1007/s10915-021-01708-4
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000738666900003
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59842
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Xiaorong
作者单位	1.Zhengzhou Univ, Henan Acad Big Data, Zhengzhou 450001, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Univ Chinese Acad Sci, LSEC,NCMIS, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Xiaodi,Wang, Xiaorong. A Fully Divergence-Free Finite Element Scheme for Stationary Inductionless Magnetohydrodynamic Equations[J]. JOURNAL OF SCIENTIFIC COMPUTING,2022,90(2):30.
APA	Zhang, Xiaodi,&Wang, Xiaorong.(2022).A Fully Divergence-Free Finite Element Scheme for Stationary Inductionless Magnetohydrodynamic Equations.JOURNAL OF SCIENTIFIC COMPUTING,90(2),30.
MLA	Zhang, Xiaodi,et al."A Fully Divergence-Free Finite Element Scheme for Stationary Inductionless Magnetohydrodynamic Equations".JOURNAL OF SCIENTIFIC COMPUTING 90.2(2022):30.