A CHARGE-CONSERVATIVE FINITE ELEMENT METHOD FOR INDUCTIONLESS MHD EQUATIONS. PART I: CONVERGENCE

doi:10.1137/17M1160768

	A CHARGE-CONSERVATIVE FINITE ELEMENT METHOD FOR INDUCTIONLESS MHD EQUATIONS. PART I: CONVERGENCE
	Li, Lingxiao 1; Ni, Mingjiu 2; Zheng, Weiying3,4
	2019
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	41 期号:4 页码:B796-B815
摘要	A charge-conservative finite element method is proposed to solve the inductionless and incompressible magnetohydrodynamic (MHD) equations in three dimensions. The method yields an exactly divergence-free current density directly. We prove that, as the spatial mesh size h -> 0, the fully discrete solutions converge to the solutions of the semicontinuous problem weakly in H-1(Omega) x H(div, Omega) upon an extracted subsequence, and as the time step size tau -> 0, the semicontinuous solutions converge to the solutions of the continuous problem weakly in L-2 (0, T; H-1(Omega))x L-2(0, T; H (div, Omega)) upon an extracted subsequence. This yields the existence of the continuous solutions naturally. Three numerical experiments are presented to show the convergence rate of discrete solutions and the charge-conservation of the method.
关键词	inductionless MHD equations block preconditioner field-of-values-equivalence conservation of charges augmented Lagrangian finite element method
DOI	10.1137/17M1160768
语种	英语
资助项目	China NSF[51636009] ; China NSF[91430215] ; National Science Fund for Distinguished Young Scholars[11725106] ; National Magnetic Confinement Fusion Science Program[2015GB110003]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000483924100033
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35576
专题	计算数学与科学工程计算研究所
通讯作者	Li, Lingxiao
作者单位	1.Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China 2.Univ Chinese Acad Sci, Sch Engn Sci, Beijing 101407, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS,LSEC, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Lingxiao,Ni, Mingjiu,Zheng, Weiying. A CHARGE-CONSERVATIVE FINITE ELEMENT METHOD FOR INDUCTIONLESS MHD EQUATIONS. PART I: CONVERGENCE[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2019,41(4):B796-B815.
APA	Li, Lingxiao,Ni, Mingjiu,&Zheng, Weiying.(2019).A CHARGE-CONSERVATIVE FINITE ELEMENT METHOD FOR INDUCTIONLESS MHD EQUATIONS. PART I: CONVERGENCE.SIAM JOURNAL ON SCIENTIFIC COMPUTING,41(4),B796-B815.
MLA	Li, Lingxiao,et al."A CHARGE-CONSERVATIVE FINITE ELEMENT METHOD FOR INDUCTIONLESS MHD EQUATIONS. PART I: CONVERGENCE".SIAM JOURNAL ON SCIENTIFIC COMPUTING 41.4(2019):B796-B815.