Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations

doi:10.1007/s10483-016-2120-8

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (8): 1095-1112.doi: https://doi.org/10.1007/s10483-016-2120-8

• 论文 • 上一篇

Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations

Chao XU¹, Dongyang SHI², Xin LIAO²

1. Faculty of Mathematics and Physics Education, Luoyang Institute of Science and Technology, Luoyang 471023, China;
2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

收稿日期:2015-10-09 修回日期:2016-03-14 出版日期:2016-08-01 发布日期:2016-08-01
通讯作者: Dongyang SHI E-mail:shi_dy@zzu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11271340)

Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations

Chao XU¹, Dongyang SHI², Xin LIAO²

1. Faculty of Mathematics and Physics Education, Luoyang Institute of Science and Technology, Luoyang 471023, China;
2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

Received:2015-10-09 Revised:2016-03-14 Online:2016-08-01 Published:2016-08-01
Contact: Dongyang SHI E-mail:shi_dy@zzu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11271340)

摘要/Abstract

摘要：

This paper studies a low order mixed finite element method (FEM) for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q₁^rot element and the piecewise constant, respectively. The superconvergent error estimates of the velocity in the broken H¹-norm and the pressure in the L²-norm are obtained respectively when the exact solutions are reasonably smooth. A numerical experiment is carried out to confirm the theoretical results.

关键词: superconvergent error estimate, nonstationary incompressible Navier-Stokes equation, constrained Q₁^rot nonconforming finite element (FE)

Abstract:

Key words: constrained Q₁^rot nonconforming finite element (FE), nonstationary incompressible Navier-Stokes equation, superconvergent error estimate

中图分类号:

65N30
65N15

Chao XU, Dongyang SHI, Xin LIAO. Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(8): 1095-1112.

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Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations

Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations

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