TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM

doi:10.1016/S0252-9602(14)60062-X

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (3): 960-972.doi: 10.1016/S0252-9602(14)60062-X

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TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM

文娟¹|何银年¹|王学敏²|霍米会¹

1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China；
2. Department of Mathematics, Texas A&M University, Colloge Station, Texas 77843, USA

收稿日期:2012-12-03 出版日期:2014-05-20 发布日期:2014-05-20

TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM

WEN Juan¹, HE Yin-Nian¹, WANG Xue-Min², HUO Mi-Hui

1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China；
2. Department of Mathematics, Texas A&M University, Colloge Station, Texas 77843, USA

Received:2012-12-03 Online:2014-05-20 Published:2014-05-20

摘要/Abstract

摘要：

In this article, on the basis of two-level discretizations and multiscale finite el-ement method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element dis-cretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.

关键词: Multiscale finite element method, two-level method, error analysis, the Navier-Stokes problem

Abstract:

Key words: Multiscale finite element method, two-level method, error analysis, the Navier-Stokes problem

文娟, 何银年, 王学敏, 霍米会. TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM[J]. 数学物理学报(英文版), 2014, 34(3): 960-972.

WEN Juan, HE Yin-Nian, WANG Xue-Min, HE Mi-Hui. TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM[J]. Acta mathematica scientia,Series B, 2014, 34(3): 960-972.

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TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM

TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM

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