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May  2010, 13(3): 665-684. doi: 10.3934/dcdsb.2010.13.665

Fully discrete finite element method for the viscoelastic fluid motion equations

Kun Wang 1, , Yinnian He 2, and  Yueqiang Shang 1,

1. 

Faculty of Science, Xi’an Jiaotong University, Xi’an 710049, China, China
2. 

Faculty of Science, Xi'an Jiaotong University, Xi'an 710049

Received  December 2008 Revised  November 2009 Published  February 2010

In this article, a fully discrete finite element method is considered for the viscoelastic fluid motion equations arising in the two-dimensional Oldroyd model. A finite element method is proposed for the spatial discretization and the time discretization is based on the backward Euler scheme. Moreover, the stability and optimal error estimates in the $L^2$- and $H^1$-norms for the velocity and $L^2$-norm for the pressure are derived for all time $t>0.$ Finally, some numerical experiments are shown to verify the theoretical predictions.
Keywords: time discretization, finite element method, Viscoelastic fluid motion equations, long-time error estimate., Oldroyd model.
Mathematics Subject Classification: Primary: 35L70, 65M30, 76D05, 78A1.
Citation: Kun Wang, Yinnian He, Yueqiang Shang. Fully discrete finite element method for the viscoelastic fluid motion equations. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 665-684. doi: 10.3934/dcdsb.2010.13.665
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