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Volume 22, Issue 1
A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations II: Time Discretization

Yinnian He, Huanling Miao & Chunfeng Ren

J. Comp. Math., 22 (2004), pp. 33-54.

Published online: 2004-02

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  • Abstract

 In this article we consider the fully discrete two-level finite element Galerkin method for the two-dimensional nonstationary incompressible Navier-Stokes equations. This method consists in dealing with the fully discrete nonlinear Navier-Stokes problem on a coarse mesh with width $H$ and the fully discrete linear generalized Stokes problem on a fine mesh with width $h << H$. Our results show that if we choose $H=O(h^{1/2}$) this method is as the same stability and convergence as the fully discrete standard finite element Galerkin method which needs dealing with the fully discrete nonlinear Navier-Stokes problem on a fine mesh with width $h$. However, our method is cheaper than the standard fully discrete finite element Galerkin method.  

  • Keywords

Navier-Stokes equations, Galerkin method, Finite element.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-33, author = {He , YinnianMiao , Huanling and Ren , Chunfeng}, title = {A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations II: Time Discretization}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {1}, pages = {33--54}, abstract = {

 In this article we consider the fully discrete two-level finite element Galerkin method for the two-dimensional nonstationary incompressible Navier-Stokes equations. This method consists in dealing with the fully discrete nonlinear Navier-Stokes problem on a coarse mesh with width $H$ and the fully discrete linear generalized Stokes problem on a fine mesh with width $h << H$. Our results show that if we choose $H=O(h^{1/2}$) this method is as the same stability and convergence as the fully discrete standard finite element Galerkin method which needs dealing with the fully discrete nonlinear Navier-Stokes problem on a fine mesh with width $h$. However, our method is cheaper than the standard fully discrete finite element Galerkin method.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8849.html} }
TY - JOUR T1 - A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations II: Time Discretization AU - He , Yinnian AU - Miao , Huanling AU - Ren , Chunfeng JO - Journal of Computational Mathematics VL - 1 SP - 33 EP - 54 PY - 2004 DA - 2004/02 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8849.html KW - Navier-Stokes equations, Galerkin method, Finite element. AB -

 In this article we consider the fully discrete two-level finite element Galerkin method for the two-dimensional nonstationary incompressible Navier-Stokes equations. This method consists in dealing with the fully discrete nonlinear Navier-Stokes problem on a coarse mesh with width $H$ and the fully discrete linear generalized Stokes problem on a fine mesh with width $h << H$. Our results show that if we choose $H=O(h^{1/2}$) this method is as the same stability and convergence as the fully discrete standard finite element Galerkin method which needs dealing with the fully discrete nonlinear Navier-Stokes problem on a fine mesh with width $h$. However, our method is cheaper than the standard fully discrete finite element Galerkin method.  

He , YinnianMiao , Huanling and Ren , Chunfeng. (2004). A Two-Level Finite Element Galerkin Method for the Nonstationary Navier-Stokes Equations II: Time Discretization. Journal of Computational Mathematics. 22 (1). 33-54. doi:
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