  In this paper, a backward Euler method 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 a priori error estimate in L2-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.
