Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

doi:10.1007/s10483-013-1720-9

Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (8): 953-970.doi: https://doi.org/10.1007/s10483-013-1720-9

Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

陈刚¹ 冯民富¹ 何银年²

1. Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China;
2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, P. R. China

出版日期:2013-07-15 发布日期:2013-07-15
通讯作者: Min-fu FENG E-mail:fmf@wtjs.cn

Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

Gang CHEN¹, Min-fu FENG¹, Yin-nian HE²

1. Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China;
2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, P. R. China

Online:2013-07-15 Published:2013-07-15
Contact: Min-fu FENG E-mail:fmf@wtjs.cn

摘要/Abstract

摘要： A unified analysis is presented for the stabilized methods including the pressure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equations. The existence and uniqueness of the solution and the optimal error estimates are proved.

关键词: 凸二次整数极小化, 随机水平值逼近, 相对熵方法, 渐进收敛性, Navier-Stokes equation, Ladyzhenskaya-Babu?ska-Brezzi (LBB) condition, low-order finite element, pressure projection method, pressure gradient local projection method

Abstract: A unified analysis is presented for the stabilized methods including the pressure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equations. The existence and uniqueness of the solution and the optimal error estimates are proved.

Key words: asymptotic convergence, quadratic integer convex programming, stochastic level value approximation, cross-entropy method, Navier-Stokes equation, Ladyzhenskaya-Babu?ska-Brezzi (LBB) condition, low-order finite element, pressure projection method, pressure gradient local projection method

陈刚冯民富何银年. Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(8): 953-970.

Gang CHEN;Min-fu FENG;Yin-nian HE. Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(8): 953-970.

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Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

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