Fully discrete finite element method for the viscoelastic fluidmotion equations

Kun Wang; Yinnian He; Yueqiang Shang

doi:10.3934/dcdsb.2010.13.665

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2010, Volume 13, Issue 3: 665-684. Doi: 10.3934/dcdsb.2010.13.665

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Fully discrete finite element method for the viscoelastic fluid motion equations

1.
Faculty of Science, Xi’an Jiaotong University, Xi’an 710049
2.
Faculty of Science, Xi'an Jiaotong University, Xi'an 710049

Received: November 30, 2008

Revised: October 31, 2009

Published: September 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 35L70, 65M30, 76D05, 78A10.

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