Mixed Finite Element Method for a Hemivariational Inequality of Stationary Navier–Stokes Equations

2021 ◽  
Vol 89 (1) ◽  
Author(s):  
Weimin Han ◽  
Kenneth Czuprynski ◽  
Feifei Jing
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Hemivariational Inequality ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations ◽  
Element Method

An Oseen-Type Post-Processed Finite Element Method Based on a Subgrid Model for the Time-Dependent Navier–Stokes Equations

2019 ◽  
Vol 17 (04) ◽  
pp. 1950002
Author(s):  
Qihui Zhang ◽  
Yueqiang Shang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Subgrid Model ◽  
Element Method

An Oseen-type post-processed mixed finite element method based on a subgrid model is presented for the simulation of time-dependent incompressible Navier–Stokes equations. This method first solves a subgrid stabilized nonlinear Navier–Stokes system on a mesh of size [Formula: see text] to obtain an approximate solution pair [Formula: see text] at the given final time [Formula: see text], and then post-processes the solution [Formula: see text] by solving a stabilized Oseen problem on a finer mesh or in higher-order finite element spaces. We prove stability of the stabilized method, derive error estimates for the post-processed solutions, give some numerical results to verify the theoretical predictions and demonstrate the effectiveness of the proposed method.

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