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Bibliographic Details
Main Authors: Bir, Bikram, Goswami, Deepjyoti, Pani, Amiya K.
Format: Preprint
Published: 2021
Subjects:
Online Access:https://arxiv.org/abs/2106.16052
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Table of Contents:
  • In this paper, a backward Euler method combined with finite element discretization in spatial direction is discussed for the equations of motion arising in the $2D$ Oldroyd model of viscoelastic fluids of order one with the forcing term independent of time or in $L^{\infty}$ in time. It is shown that the estimates of the discrete solution in Dirichlet norm is bounded uniformly in time. Optimal {\it a priori} error estimate in $\textbf{L}^2$-norm is derived for the discrete problem with non-smooth initial data. This estimate is shown to be uniform in time, under the assumption of uniqueness condition. Finally, we present some numerical results to validate our theoretical results.