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Backward Euler method for the equations of motion arising in Oldroyd model of order one with nonsmooth initial data
Journal
IMA Journal of Numerical Analysis
ISSN
02724979
Date Issued
2022-10-01
Author(s)
Bir, Bikram
Goswami, Deepjyoti
Pani, Amiya K.
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 two-dimensional Oldroyd model of viscoelastic fluids of order one with the forcing term independent of time or in L∞ in time. It is shown that the estimates of the discrete solution in Dirichlet norm is bounded uniformly in time. Optimal a priori error estimate in bf L2-norm is derived for the discrete problem with nonsmooth 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.
Volume
42
Publication link
Subjects