# American Institute of Mathematical Sciences

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

## Fully discrete finite element method for the viscoelastic fluid motion equations

 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.
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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