Fully discrete finite element method based on pressure stabilization for the transient Stokes equations

Fully discrete finite element method based on pressure stabilization for the transient Stokes equations

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Article ID: iaor20123988
Volume: 82
Issue: 8
Start Page Number: 1496
End Page Number: 1515
Publication Date: Apr 2012
Journal: Mathematics and Computers in Simulation
Authors: ,
Keywords: integration, fluid models
Abstract:

In this work, a new fully discrete stabilized finite element method is studied for the two‐dimensional transient Stokes equations. This method is to use the difference between a consistent mass matrix and underintegrated mass matrix as the complement for the pressure. The spatial discretization is based on the P 1P 1 triangular element for the approximation of the velocity and pressure, the time discretization is based on the Euler semi‐implicit scheme. Some error estimates for the numerical solutions of fully discrete stabilized finite element method are derived. Finally, we provide some numerical experiments, compared with other methods, we can see that this novel stabilized method has better stability and accuracy results for the unsteady Stokes problem.

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