非定常Navier-Stokes方程的一种非线性局部投影稳定化有限元方法  

A nonlinear local projection-based finite element method for unsteady Navier-Stokes equations

作　　者：李西 罗加福 冯民富[1] LI Xi;LUO Jia-Fu;FENG Min-Fu(School of Mathematics,Sichuan University,Chengdu 610064,China;Chengdu Sports University,Chengdu 610041,China)

机构地区：[1]四川大学数学学院,成都610064 [2]成都体育学院,成都610041

出　　处：《四川大学学报（自然科学版）》2021年第3期8-16,共9页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11971337,11271273)。

摘　　要：针对非定常Navier-Stokes方程,本文提出了一种基于非线性对流项和压力梯度的局部投影稳定化有限元方法.该方法在空间上采用等阶有限元,时间上采用隐式有限差分.本文建立了非定常Navier-Stokes方程的全离散数值格式,进而分析了离散解的稳定性和收敛性.值得注意的是,该方法中得到的误差估计随着流体雷诺数的增大依然有效.In this study,a stable local projection finite element method is proposed for unsteady Navier-Stokes equations.This method is formed by local projection of advection term and pressure gradient.By using the equal-order conforming finite elements in space and implicit finite difference scheme in time,we derive a fully discrete formulation and obtain the stability and convergence of the approximation solution.Notably,the error estimates hold even for large Reynolds numbers.

关 键 词：非定常Navier-Stokes方程 局部投影 雷诺数 非inf-sup稳定 

分 类 号：O241.82[理学—计算数学]