Backward Euler method for the equations of motion arising in Oldroyd model of order one with nonsmooth initial data
| Autor: | Bir, Bikram, Goswami, Deepjyoti, Pani, Amiya K. |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 30 pages, 15 figure. arXiv admin note: substantial text overlap with arXiv:1208.6343 |
| Databáze: | arXiv |
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