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

Authors:
Tong Zhang;Yinnian He
Affiliations:
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, PR China and Center for Computational Geosciences, School of Mathematics and Statistics, Xi'an Jiaotong ...;Center for Computational Geosciences, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, PR China
Venue:
Mathematics and Computers in Simulation
Year:
2012

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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"1-P"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.