Error analysis of a conservative finite element scheme for time-dependent inductionless MHD problem

doi:10.1016/j.cam.2022.114728

	Error analysis of a conservative finite element scheme for time-dependent inductionless MHD problem
	Long, Xiaonian 1; Ding, Qianqian 2; Mao, Shipeng 3,4
刊名	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
	2023-02-01
卷号	419 页码:22
关键词	Inductionless magnetohydrodynamics Current density conservation Euler semi-implicit Error estimate Mixed finite element method
ISSN号	0377-0427
DOI	10.1016/j.cam.2022.114728
英文摘要	In this paper, we develop and analyze a fully discrete mixed finite element method for unsteady inductionless magnetohydrodynamics problem. An Euler semi-implicit scheme is proposed with a mixed variational formulation based on the variables (u, p, j, phi), in which the Navier-Stokes equations are approximated by stable finite elements and the current density is discretized by the divergence-conforming finite element. This scheme has the feature that the discrete current density keeps charge conservation property. It is shown that both the continuous problem and its fully discrete Euler semi-implicit scheme are well-posed. We prove unconditionally convergence and error estimates for velocity, pressure and current density. Finally, numerical experiments have been performed to validate the theoretical analysis and the law of charge conservation. (c) 2022 Elsevier B.V. All rights reserved.
资助项目	National Natural Science Foundation of China[11871467] ; National Natural Science Foundation of China[12161141017]
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000863214300005
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60877]
专题	中国科学院数学与系统科学研究院
通讯作者	Mao, Shipeng
作者单位	1.Henan Univ Econ & Law, Coll Math & Informat Sci, Zhengzhou 450047, Peoples R China 2.Shandong Univ, Sch Math, Jinan 250100, Peoples R China 3.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, NCMIS, 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	Long, Xiaonian,Ding, Qianqian,Mao, Shipeng. Error analysis of a conservative finite element scheme for time-dependent inductionless MHD problem[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2023,419:22.
APA	Long, Xiaonian,Ding, Qianqian,&Mao, Shipeng.(2023).Error analysis of a conservative finite element scheme for time-dependent inductionless MHD problem.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,419,22.
MLA	Long, Xiaonian,et al."Error analysis of a conservative finite element scheme for time-dependent inductionless MHD problem".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 419(2023):22.