3维非定常Navier-Stokes方程组高效全离散有限元方法研究进展

何银年; 冯新龙

doi:10.13568/j.cnki.651094.651316.2022.04.09.0001

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3维非定常Navier-Stokes方程组高效全离散有限元方法研究进展

研究精粹 | 更新时间：2026-01-21

- 3维非定常Navier-Stokes方程组高效全离散有限元方法研究进展
- 3维非定常Navier-Stokes方程组高效全离散有限元方法研究进展
- 新疆大学学报（自然科学版中英文） 2022年39卷第3期页码：257-265
- 作者机构：
  
  1. 新疆大学数学与系统科学学院
  2. 西安交通大学数学与统计学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金（11771348;12001466;12071406;U19A2079）
- DOI：10.13568/j.cnki.651094.651316.2022.04.09.0001
  中图分类号： O241.82
- 纸质出版：2022
- 稿件说明：
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[1]何银年,冯新龙.3维非定常Navier-Stokes方程组高效全离散有限元方法研究进展[J].新疆大学学报(自然科学版)(中英文),2022,39(03):257-265.
[1]何银年,冯新龙.3维非定常Navier-Stokes方程组高效全离散有限元方法研究进展[J].新疆大学学报(自然科学版)(中英文),2022,39(03):257-265. DOI： 10.13568/j.cnki.651094.651316.2022.04.09.0001.

DOI：10.13568/j.cnki.651094.651316.2022.04.09.0001.

摘要

针对数值求解3维非定常Navier-Stokes方程组时面临的不可压缩条件、非线性和长时间积分性等困难

讨论了能够克服这些困难的高效全离散有限元方法的研究现状和最新研究成果.此外

也阐述了求解3维非定常Navier-Stokes方程组的有限元空间离散解的稳定性、误差估计和高效全离散有限元解的最优误差估计.

Abstract

Main difficulties of numerically solving the 3D time-dependent Navier-Stokes equations are incompressibility condition

nonlinearity and longtime integration. First

we discuss the research progress and recent achievements in the highly efficient fully discrete finite element method for solving the 3D time-dependent NavierStokes equations. Secondly

we expound the stability and error estimates of the finite element spatial discrete solution and the optimal error estimates of the highly efficient fully discrete finite element method for solving the3D time-dependent Navier-Stokes equations.

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references

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