Decoupled modified characteristics finite element method for the time dependent Navier-Stokes/Darcy problem

2013 ◽  
Vol 37 (9) ◽  
pp. 1392-1404 ◽  
Author(s):  
Zhiyong Si ◽  
Yunxia Wang ◽  
Shishun Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Time Dependent ◽  
Navier Stokes ◽  
Darcy Problem ◽  
Element Method

scholarly journals A Two-Grid Finite Element Method for Time-Dependent Incompressible Navier-Stokes Equations with Non-Smooth Initial Data

2015 ◽  
Vol 8 (4) ◽  
pp. 549-581 ◽  
Author(s):  
Deepjyoti Goswami ◽  
Pedro D. Damázio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Initial Data ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Smooth Initial Data ◽  
Element Method

AbstractWe analyze here, a two-grid finite element method for the two dimensional time-dependent incompressible Navier-Stokes equations with non-smooth initial data. It involves solving the non-linear Navier-Stokes problem on a coarse grid of size H and solving a Stokes problem on a fine grid of size h, h « H. This method gives optimal convergence for velocity in H1-norm and for pressure in L2-norm. The analysis mainly focuses on the loss of regularity of the solution at t = 0 of the Navier-Stokes equations.

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