In this paper, we present a decoupled finite element scheme for twodimensional
time-dependent viscoelastic fluid flow obeying an Oldroyd-B constitutive
equation. The key idea of our decoupled scheme is to divide the full problem into
two subproblems, one is the constitutive equation which is stabilized by using discontinuous
Galerkin (DG) approximation, and the other is the Stokes problem, can be
computed parallel. The decoupled scheme can reduce the computational cost of the
numerical simulation and implementation is easy. We compute the velocity u and the
pressure p from the Stokes like problem, another unknown stress σ from the constitutive
equation. The approximation of stress, velocity and pressure are respectively, P_{1}-
discontinuous, P_{2}-continuous, and P_{1}-continuous finite elements. The well-posedness
of the finite element scheme is presented and derive the stability analysis of the decoupled
algorithm. We obtain the desired error bound also demonstrate the order of the
convergence, stability and the flow behavior with the support of two numerical experiments
which reveals that decoupled scheme is more efficient than coupled scheme.