数学季刊 >

2017 , Vol. 32 >Issue 1: 88 - 98

DOI: https://doi.org/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

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

收稿日期: 2016-10-23

  网络出版日期: 2020-10-26

基金资助

Supported by the National Natural Science Foundation of China(11271340,116713697)； Supported by Henan Natural Science Foundation of China(132300410376)；

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

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

Received date: 2016-10-23

  Online published: 2020-10-26

Supported by

Supported by the National Natural Science Foundation of China(11271340,116713697)； Supported by Henan Natural Science Foundation of China(132300410376)；

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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

本文引用格式

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

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

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