Asymptotic analysis of the equations ofmotion for viscoelastic oldroyd fluid

In this paper, the asymptotic analysis of the two-dimensional viscoelastic Oldroyd flows is presented. With the physical constant ρ/δ approaches zero, where ρ is the viscoelastic coefficient and 1/δ the relaxation time, the viscoelastic Oldroyd fluid motion equations converge to the viscous model known as the famous Navier-Stokes equations. Both the continuous and discrete uniform-in-time asymptotic errors are provided. Finally, the theoretical predictions are confirmed by some numerical experiments.