A fully divergence-free finite element method for magnetohydrodynamic equations

doi:10.1142/S0218202518500173

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	A fully divergence-free finite element method for magnetohydrodynamic equations
	Hiptmair, Ralf 1; Li, Lingxiao 2; Mao, Shipeng2 ; Zheng, Weiying2
刊名	MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
	2018-04-01
卷号	28 期号:4 页码:659-695
关键词	Magnetohydrodynamic equations divergence-free finite element method preconditioner magnetic vector potential driven cavity flow
ISSN号	0218-2025
DOI	10.1142/S0218202518500173
英文摘要	We propose a finite element method for the three-dimensional transient incompressible magnetohydrodynamic equations that ensures exactly divergence-free approximations of the velocity and the magnetic induction. We employ second-order semi-implicit timestepping, for which we rigorously establish an energy law and, as a consequence, unconditional stability. We prove unique solvability of the linear systems of equations to be solved in every timestep. For those we design an efficient preconditioner so that the number of preconditioned GMRES iterations is uniformly bounded with respect to the number of degrees of freedom. As both meshwidth and timestep size tend to zero, we prove that the discrete solutions converge to a weak solution of the continuous problem. Finally, by several numerical experiments, we confirm the predictions of the theory and demonstrate the efficiency of the preconditioner.
资助项目	National Center for Mathematics and Interdisciplinary Sciences of China ; State Key Laboratory of Scientific and Engineering Computing of China ; National Magnetic Confinement Fusion Science Program of China[2015GB110003] ; National Key Research and Development Program of China[2016YFB0201304] ; China NSF[11471329] ; China NSF[91430215] ; Youth Innovation Promotion Association of CAS[2016003] ; National Science Fund for Distinguished Young Scholars[11725106]
WOS研究方向	Mathematics
语种	英语
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
WOS记录号	WOS:000432721600002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/30359]
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.Swiss Fed Inst Technol, Seminar Appl Math, CH-8092 Zurich, Switzerland 2.Chinese Acad Sci, Sch Math Sci, Acad Math & Syst Sci, NCMIS,LSEC,ICMSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Hiptmair, Ralf,Li, Lingxiao,Mao, Shipeng,et al. A fully divergence-free finite element method for magnetohydrodynamic equations[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES,2018,28(4):659-695.
APA	Hiptmair, Ralf,Li, Lingxiao,Mao, Shipeng,&Zheng, Weiying.(2018).A fully divergence-free finite element method for magnetohydrodynamic equations.MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES,28(4),659-695.
MLA	Hiptmair, Ralf,et al."A fully divergence-free finite element method for magnetohydrodynamic equations".MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES 28.4(2018):659-695.