Fully discrete finite element method for the viscoelastic fluid motion equations

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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

Abstract
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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 & Continuous Dynamical Systems - B, 2010, 13 (3) : 665-684. doi: 10.3934/dcdsb.2010.13.665

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