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