- Journal Home
- Volume 42 - 2024
- Volume 41 - 2023
- Volume 40 - 2022
- Volume 39 - 2021
- Volume 38 - 2020
- Volume 37 - 2019
- Volume 36 - 2018
- Volume 35 - 2017
- Volume 34 - 2016
- Volume 33 - 2015
- Volume 32 - 2014
- Volume 31 - 2013
- Volume 30 - 2012
- Volume 29 - 2011
- Volume 28 - 2010
- Volume 27 - 2009
- Volume 26 - 2008
- Volume 25 - 2007
- Volume 24 - 2006
- Volume 23 - 2005
- Volume 22 - 2004
- Volume 21 - 2003
- Volume 20 - 2002
- Volume 19 - 2001
- Volume 18 - 2000
- Volume 17 - 1999
- Volume 16 - 1998
- Volume 15 - 1997
- Volume 14 - 1996
- Volume 13 - 1995
- Volume 12 - 1994
- Volume 11 - 1993
- Volume 10 - 1992
- Volume 9 - 1991
- Volume 8 - 1990
- Volume 7 - 1989
- Volume 6 - 1988
- Volume 5 - 1987
- Volume 4 - 1986
- Volume 3 - 1985
- Volume 2 - 1984
- Volume 1 - 1983
Cited by
- BibTex
- RIS
- TXT
A global finite element nonlinear Galerkin method for the penalized Navier-Stokes equations is presented. This method is based on two finite element spaces $X_H$ and $X_h$, defined respectively on one coarse grid with grid size $H$ and one fine grid with grid size $h<<H$. Comparison is also made with the finite element Galerkin method. If we choose $H=O(ε^{-1/4}h^{1/2}), ε>0$ being the penalty parameter, then two methods are of the same order of approximation. However, the global finite element nonlinear Galerkin method is much cheaper than the standard finite element Galerkin method. In fact, in the finite element Galerkin method the nonlinearity is treated on the fine grid finite element space $X_h$ and while in the global finite element nonlinear Galerkin method the similar nonlinearity is treated on the coarse grid finite element space $X_H$ and only the linearity needs to be treated on the fine grid increment finite element space $W_h$. Finally, we provide numerical test which shows above results stated.
}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9013.html} }A global finite element nonlinear Galerkin method for the penalized Navier-Stokes equations is presented. This method is based on two finite element spaces $X_H$ and $X_h$, defined respectively on one coarse grid with grid size $H$ and one fine grid with grid size $h<<H$. Comparison is also made with the finite element Galerkin method. If we choose $H=O(ε^{-1/4}h^{1/2}), ε>0$ being the penalty parameter, then two methods are of the same order of approximation. However, the global finite element nonlinear Galerkin method is much cheaper than the standard finite element Galerkin method. In fact, in the finite element Galerkin method the nonlinearity is treated on the fine grid finite element space $X_h$ and while in the global finite element nonlinear Galerkin method the similar nonlinearity is treated on the coarse grid finite element space $X_H$ and only the linearity needs to be treated on the fine grid increment finite element space $W_h$. Finally, we provide numerical test which shows above results stated.