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arXiv · 2106.16052

Backward Euler method for the equations of motion arising in Oldroyd model of order one with nonsmooth initial data

Bikram Bir·Deepjyoti Goswami·Amiya K. Pani
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Abstract

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.

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Bikram Bir, Deepjyoti Goswami, Amiya K. Pani. 2021-06-30. Backward Euler method for the equations of motion arising in Oldroyd model of order one with nonsmooth initial data. https://doi.org/10.1093/imanum%2Fdrab072

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