A Finite Element Variational Multiscale Method for the Navier--Stokes Equations

2005 ◽  
Vol 26 (5) ◽  
pp. 1485-1503 ◽  
Author(s):  
Volker John ◽  
Songul Kaya
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Multiscale Method ◽  
Navier Stokes ◽  
Variational Multiscale Method ◽  
Navier Stokes Equations ◽  
Variational Multiscale

scholarly journals A Multilevel Finite Element Variational Multiscale Method for Incompressible Navier-Stokes Equations Based on Two Local Gauss Integrations

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Yamiao Zhang ◽  
Biwu Huang ◽  
Jiazhong Zhang ◽  
Zexia Zhang
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Main Idea ◽  
Multiscale Method ◽  
Navier Stokes ◽  
Variational Multiscale Method ◽  
Time Saving ◽  
Navier Stokes Equations ◽  
Variational Multiscale ◽  
The Stability

A multilevel finite element variational multiscale method is proposed and applied to the numerical simulation of incompressible Navier-Stokes equations. This method combines the finite element variational multiscale method based on two local Gauss integrations with the multilevel discretization using Newton correction on each step. The main idea of the multilevel finite element variational multiscale method is that the equations are first solved on a single coarse grid by finite element variational multiscale method; then finite element variational multiscale approximations are generated on a succession of refined grids by solving a linearized problem. Moreover, the stability analysis and error estimate of the multilevel finite element variational multiscale method are given. Finally, some numerical examples are presented to support the theoretical analysis and to check the efficiency of the proposed method. The results show that the multilevel finite element variational multiscale method is more efficient than the one-level finite element variational multiscale method, and for an appropriate choice of meshes, the multilevel finite element variational multiscale method is not only time-saving but also highly accurate.

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