定常Navier-Stokes方程的一个二阶非协调三角型混合元格式

doi:10.13371/j.cnki.chin.q.j.m.2017.01.010

数学季刊 ›› 2017, Vol. 32 ›› Issue (1): 88-98.doi: 10.13371/j.cnki.chin.q.j.m.2017.01.010

定常Navier-Stokes方程的一个二阶非协调三角型混合元格式

School of Mathematics and Statistics,Zhengzhou Normal University. School of Science,Henan Institute of Engineering. School of Mathematics and Statistics,Zhengzhou University

收稿日期:2016-10-23 出版日期:2017-03-30 发布日期:2020-10-26
作者简介:WANG Zhi-jun(1969-), male, native of Xingyang, Henan, an associate professor of Zhengzhou Normal University, engages in finite element method and application; HAO Xiao-bin(1974-), male, native of Pingdingshan, Henan, a lecturer of Henan Institute of Engineering, engages in finite element method and application; SHI Dong-yang(1961-), male, native of Lushan, Henan, a professor of Zhengzhou University, engages in finite element method and application.
基金资助:
Supported by the National Natural Science Foundation of China(11271340,116713697)； Supported by Henan Natural Science Foundation of China(132300410376)；

A Second Order Nonconforming Triangular Mixed Finite Element Scheme for the Stationary Navier-Stokes Equations

School of Mathematics and Statistics,Zhengzhou Normal University. School of Science,Henan Institute of Engineering. School of Mathematics and Statistics,Zhengzhou University

Received:2016-10-23 Online:2017-03-30 Published:2020-10-26
About author:WANG Zhi-jun(1969-), male, native of Xingyang, Henan, an associate professor of Zhengzhou Normal University, engages in finite element method and application; HAO Xiao-bin(1974-), male, native of Pingdingshan, Henan, a lecturer of Henan Institute of Engineering, engages in finite element method and application; SHI Dong-yang(1961-), male, native of Lushan, Henan, a professor of Zhengzhou University, engages in finite element method and application.
Supported by:
Supported by the National Natural Science Foundation of China(11271340,116713697)； Supported by Henan Natural Science Foundation of China(132300410376)；

摘要/Abstract

摘要： In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure. The convergence analysis is presented and optimal error estimates of both broken H¹-norm and L²-norm for velocity as well as the L²-norm for the pressure are derived.

关键词: stationary Navier-Stokes equations, nonconforming triangular mixed finite element scheme, optimal error estimates

Abstract: In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure. The convergence analysis is presented and optimal error estimates of both broken H¹-norm and L²-norm for velocity as well as the L²-norm for the pressure are derived.

Key words: stationary Navier-Stokes equations, nonconforming triangular mixed finite element scheme, optimal error estimates

中图分类号:

O241.82

王志军, 郝晓斌, 石东洋. 定常Navier-Stokes方程的一个二阶非协调三角型混合元格式[J]. 数学季刊, 2017, 32(1): 88-98.

WANG Zhi-jun, HAO Xiao-bin, SHI Dong-yang. A Second Order Nonconforming Triangular Mixed Finite Element Scheme for the Stationary Navier-Stokes Equations[J]. Chinese Quarterly Journal of Mathematics, 2017, 32(1): 88-98.

[1]	王金凤, 刘洋, 李宏. 粘弹性波动方程的H¹-Galerkin混合有限元方法误差估计[J]. 数学季刊, 2011, 26(1): 131-137.
[2]	王波, 王强. 非线性抛物型积分-微分方程的向后Euler差分有限体积元方法[J]. 数学季刊, 2009, 24(3): 370-377.

定常Navier-Stokes方程的一个二阶非协调三角型混合元格式

A Second Order Nonconforming Triangular Mixed Finite Element Scheme for the Stationary Navier-Stokes Equations

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