@Article{IJNAM-14-1,
author = {},
title = {Backward Euler Schemes for the Kelvin-Voigt Viscoelastic Fluid Flow Model},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2017},
volume = {14},
number = {1},
pages = {126--151},
abstract = {<p style="text-align: justify; margin-bottom: 10px;">In this paper, we discuss the backward Euler method along with its linearized version
for the Kelvin-Voigt viscoelastic fluid flow model with non zero forcing function, which is either
independent of time or in $\rm{L}^∞(\rm{L^2})$. After deriving some bounds for the semidiscrete scheme,
a priori estimates in Dirichlet norm for the fully discrete scheme are obtained, which are valid
uniformly in time using a combination of discrete Gronwall&#39;s lemma and Stolz-Cesaro&#39;s classical
result for sequences. Moreover, an existence of a discrete global attractor for the discrete problem
is established. Further, optimal a priori error estimates are derived, whose bounds may depend
exponentially in time. Under uniqueness condition, these estimates are shown to be uniform
in time. Even when $\rm{f}$ = 0, the present result improves upon earlier result of Bajpai et al.
(IJNAM,10 (2013), pp.481-507) in the sense that error bounds in this article depend on $1 / \sqrt{\kappa}$ as
against $1 / \kappa^r$, $r \geq 1$. Finally, numerical experiments are conducted which confirm our theoretical
findings.</p>},
issn = {2617-8710},
doi = {https://doi.org/2017-IJNAM-414},
url = {https://global-sci.com/article/83161/backward-euler-schemes-for-the-kelvin-voigt-viscoelastic-fluid-flow-model}
}