THE TWO-LEVEL STABILIZED FINITE ELEMENT METHOD BASED ON MULTISCALE ENRICHMENT FOR THE STOKES EIGENVALUE PROBLEM

doi:10.1007/s10473-021-0204-3

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (2): 381-396.doi: 10.1007/s10473-021-0204-3

THE TWO-LEVEL STABILIZED FINITE ELEMENT METHOD BASED ON MULTISCALE ENRICHMENT FOR THE STOKES EIGENVALUE PROBLEM

文娟^1,2, 黄鹏展³, 何雅玲^1,2

1. Key Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China;
2. School of Sciences, Xi'an University of Technology, Xi'an 710048, China;
3. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China

收稿日期:2019-04-12 修回日期:2020-04-23 出版日期:2021-04-25 发布日期:2021-04-29
通讯作者: Juan WEN E-mail:zhongnanjicuan@163.com
作者简介:Pengzhan HUANG,E-mail:hpzh007@yahoo.com;Ya-Ling HE,E-mail:yalinghe@mail.xjtu.edu.cn
基金资助:
This work was supported by the National Key R&D Program of China (2018YFB1501001), the NSF of China (11771348), China Postdoctoral Science Foundation (2019M653579)

THE TWO-LEVEL STABILIZED FINITE ELEMENT METHOD BASED ON MULTISCALE ENRICHMENT FOR THE STOKES EIGENVALUE PROBLEM

Juan WEN^1,2, Pengzhan HUANG³, Ya-Ling HE^1,2

1. Key Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China;
2. School of Sciences, Xi'an University of Technology, Xi'an 710048, China;
3. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China

Received:2019-04-12 Revised:2020-04-23 Online:2021-04-25 Published:2021-04-29
Contact: Juan WEN E-mail:zhongnanjicuan@163.com
About author:Pengzhan HUANG,E-mail:hpzh007@yahoo.com;Ya-Ling HE,E-mail:yalinghe@mail.xjtu.edu.cn
Supported by:
This work was supported by the National Key R&D Program of China (2018YFB1501001), the NSF of China (11771348), China Postdoctoral Science Foundation (2019M653579)

摘要/Abstract

摘要： In this paper, we first propose a new stabilized finite element method for the Stokes eigenvalue problem. This new method is based on multiscale enrichment, and is derived from the Stokes eigenvalue problem itself. The convergence of this new stabilized method is proved and the optimal priori error estimates for the eigenfunctions and eigenvalues are also obtained. Moreover, we combine this new stabilized finite element method with the two-level method to give a new two-level stabilized finite element method for the Stokes eigenvalue problem. Furthermore, we have proved a priori error estimates for this new two-level stabilized method. Finally, numerical examples confirm our theoretical analysis and validate the high effectiveness of the new methods.

关键词: Two-level, multiscale finite element method, $P_{1}/P_{1}$ elements, the Stokes eigenvalue problem

Abstract: In this paper, we first propose a new stabilized finite element method for the Stokes eigenvalue problem. This new method is based on multiscale enrichment, and is derived from the Stokes eigenvalue problem itself. The convergence of this new stabilized method is proved and the optimal priori error estimates for the eigenfunctions and eigenvalues are also obtained. Moreover, we combine this new stabilized finite element method with the two-level method to give a new two-level stabilized finite element method for the Stokes eigenvalue problem. Furthermore, we have proved a priori error estimates for this new two-level stabilized method. Finally, numerical examples confirm our theoretical analysis and validate the high effectiveness of the new methods.

Key words: Two-level, multiscale finite element method, $P_{1}/P_{1}$ elements, the Stokes eigenvalue problem

中图分类号:

35Q30

文娟, 黄鹏展, 何雅玲. THE TWO-LEVEL STABILIZED FINITE ELEMENT METHOD BASED ON MULTISCALE ENRICHMENT FOR THE STOKES EIGENVALUE PROBLEM[J]. 数学物理学报(英文版), 2021, 41(2): 381-396.

Juan WEN, Pengzhan HUANG, Ya-Ling HE. THE TWO-LEVEL STABILIZED FINITE ELEMENT METHOD BASED ON MULTISCALE ENRICHMENT FOR THE STOKES EIGENVALUE PROBLEM[J]. Acta mathematica scientia,Series B, 2021, 41(2): 381-396.

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THE TWO-LEVEL STABILIZED FINITE ELEMENT METHOD BASED ON MULTISCALE ENRICHMENT FOR THE STOKES EIGENVALUE PROBLEM

THE TWO-LEVEL STABILIZED FINITE ELEMENT METHOD BASED ON MULTISCALE ENRICHMENT FOR THE STOKES EIGENVALUE PROBLEM

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