Error Estimate of a Fully Discrete Finite Element Method for Incompressible Vector Potential Magnetohydrodynamic System

doi:10.1007/s10915-021-01571-3

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	Error Estimate of a Fully Discrete Finite Element Method for Incompressible Vector Potential Magnetohydrodynamic System
	Ding, Qianqian 1,4; Long, Xiaonian 2,4; Mao, Shipeng 3,4
	2021-09-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	88 期号:3 页码:24
摘要	We investigate a fully discrete finite element scheme for the three-dimensional incompressible magnetohydrodynamic problem based on magnetic vector potential formulation that was introduced in Hiptmair et al. (MMMAS 28:659-695, 2018). The formulation enjoys the novel feature that it can always produce an exactly divergence-free magnetic induction discretized solution. Using a mixed finite element approach, we discretize the model by the fully discrete semi-implicit Euler scheme with the velocity and the pressure approximated by stable MINI finite elements and the magnetic vector potential by Nedelec edge elements. Under a reasonable regularity hypothesis for the exact solution, error estimates for the velocity and the magnetic vector potential are rigorously established. Finally, several numerical experiments are presented to illustrate the convergence properties of the numerical scheme.
关键词	Magnetohydrodynamic Magnetic vector potential Finite element method Error estimates
DOI	10.1007/s10915-021-01571-3
收录类别	SCI
语种	英语
资助项目	China Postdoctoral Science Foundation[2021M691951] ; National Natural Science Foundation of China[11871467] ; Major State Research Development Program of China[2016YFB0201304]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000692729000001
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/59240
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.Shandong Univ, Sch Math, Jinan 250100, Peoples R China 2.Henan Univ Econ & Law, Coll Math & Informat Sci, Zhengzhou 450047, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Enginnering Comp, LSEC,NCMIS, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Ding, Qianqian,Long, Xiaonian,Mao, Shipeng. Error Estimate of a Fully Discrete Finite Element Method for Incompressible Vector Potential Magnetohydrodynamic System[J]. JOURNAL OF SCIENTIFIC COMPUTING,2021,88(3):24.
APA	Ding, Qianqian,Long, Xiaonian,&Mao, Shipeng.(2021).Error Estimate of a Fully Discrete Finite Element Method for Incompressible Vector Potential Magnetohydrodynamic System.JOURNAL OF SCIENTIFIC COMPUTING,88(3),24.
MLA	Ding, Qianqian,et al."Error Estimate of a Fully Discrete Finite Element Method for Incompressible Vector Potential Magnetohydrodynamic System".JOURNAL OF SCIENTIFIC COMPUTING 88.3(2021):24.