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

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  • Zhang, Tong
  • He, Yinnian

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 P1–P1 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.

Suggested Citation

  • Zhang, Tong & He, Yinnian, 2012. "Fully discrete finite element method based on pressure stabilization for the transient Stokes equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1496-1515.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:8:p:1496-1515
    DOI: 10.1016/j.matcom.2012.02.007
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