A higher order Galerkin finite element scheme for simulation of two‐dimensional viscoelastic
fluid flows has been developed. The numerical scheme used in this study gives rise to a
stable discretization of the continuum problem as well as providing an exponential
convergence rate toward the exact solution. Hence, with this method, spurious oscillatory
modes are effectively eliminated by increasing the order of the interpolant within each
subdomain. In our calculations, an upper limit for the Weissenberg number due to numerical …