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Error analysis of a conservative finite element scheme for time-dependent inductionless MHD problem
Long, Xiaonian1; Ding, Qianqian2; Mao, Shipeng3,4
2023-02-01
Source PublicationJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN0377-0427
Volume419Pages:22
AbstractIn 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.
KeywordInductionless magnetohydrodynamics Current density conservation Euler semi-implicit Error estimate Mixed finite element method
DOI10.1016/j.cam.2022.114728
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[11871467] ; National Natural Science Foundation of China[12161141017]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000863214300005
PublisherELSEVIER
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/60878
Collection中国科学院数学与系统科学研究院
Corresponding AuthorMao, Shipeng
Affiliation1.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
Recommended Citation
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.
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