KMS Of Academy of mathematics and systems sciences, CAS
| A Fully Divergence-Free Finite Element Scheme for Stationary Inductionless Magnetohydrodynamic Equations | |
| Zhang, Xiaodi1; Wang, Xiaorong2,3 | |
| 2022-02-01 | |
| Source Publication | JOURNAL OF SCIENTIFIC COMPUTING
 |
| ISSN | 0885-7474 |
| Volume | 90Issue:2Pages:30 |
| Abstract | In this paper, we propose and analyze a mixed finite element scheme for stationary inductionless magnetohydrodynamic equations on a general Lipschitz domain. We adopt divergence-conforming elements for the velocity and the current density, discontinuous elements for the pressure and the electric potential, thus the approximations for velocity and current density are exactly divergence-free. The H-1-continuity of the velocity is enforced by discontinuous Galerkin approach. With this discretization, we prove the well-posedness of the discrete scheme, and derive optimal error estimates of the discrete solutions. In particular, we show that the error estimates for the velocity and the current density are independent of the pressure and the electric potential, and the error estimates for the pressure and the electric potential are also unrelated to each other. Based on this, we propose two coupled iterative methods: Stokes and Oseen iterations. Rigorous analysis of convergence and stability is provided. Finally, some numerical examples are performed to verify the theoretical results and show the effectiveness of the presented methods. |
| Keyword | Mixed finite element method Divergence-free Inductionless MHD equations Conservation of charge and mass |
| DOI | 10.1007/s10915-021-01708-4 |
| Indexed By | SCI |
| Language | 英语 |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000738666900003 |
| Publisher | SPRINGER/PLENUM PUBLISHERS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59842 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Wang, Xiaorong |
| Affiliation | 1.Zhengzhou Univ, Henan Acad Big Data, Zhengzhou 450001, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Univ Chinese Acad Sci, LSEC,NCMIS, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Zhang, Xiaodi,Wang, Xiaorong. A Fully Divergence-Free Finite Element Scheme for Stationary Inductionless Magnetohydrodynamic Equations[J]. JOURNAL OF SCIENTIFIC COMPUTING,2022,90(2):30. |
| APA | Zhang, Xiaodi,&Wang, Xiaorong.(2022).A Fully Divergence-Free Finite Element Scheme for Stationary Inductionless Magnetohydrodynamic Equations.JOURNAL OF SCIENTIFIC COMPUTING,90(2),30. |
| MLA | Zhang, Xiaodi,et al."A Fully Divergence-Free Finite Element Scheme for Stationary Inductionless Magnetohydrodynamic Equations".JOURNAL OF SCIENTIFIC COMPUTING 90.2(2022):30. |
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