scholarly journals A nonconforming finite element method for the Stokes equations using the Crouzeix-Raviart element for the velocity and the standard linear element for the pressure

2013 ◽  
Vol 74 (3) ◽  
pp. 222-228 ◽  
Author(s):  
Bishnu P. Lamichhane
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Nonconforming Finite Element ◽  
Linear Element ◽  
Nonconforming Finite Element Method ◽  
Standard Linear ◽  
Element Method

scholarly journals Stabilized Multiscale Nonconforming Finite Element Method for the Stationary Navier-Stokes Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-27
Author(s):  
Tong Zhang ◽  
Shunwei Xu ◽  
Jien Deng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Navier Stokes ◽  
Optimal Order ◽  
Nonconforming Finite Element ◽  
Polynomial Space ◽  
Nonconforming Finite Element Method ◽  
Element Method

We consider a stabilized multiscale nonconforming finite element method for the two-dimensional stationary incompressible Navier-Stokes problem. This method is based on the enrichment of the standard polynomial space for the velocity component with multiscale function and the nonconforming lowest equal-order finite element pair. Stability and existence uniqueness of the numerical solution are established, optimal-order error estimates are also presented. Finally, some numerical results are presented to validate the performance of the proposed method.

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