Fully discrete finite element method for the viscoelastic fluid motion equations
Kun Wang Yinnian He Yueqiang Shang
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

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