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

WANG Zhi-jun, HAO Xiao-bin, SHI Dong-yang

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

Chinese Quarterly Journal of Mathematics >

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

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2017.01.010

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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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

Cite this article

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

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