The Discrete Elastic Viscous Stress Splitting Technique in combination with the Discontinuous Galerkin (DEVSS/DG) method is used to simulate a low density polyethylene melt flowing in a transient contraction flow problem. Numerical results using the original and a modified form of the eXtended Pom-Pom (XPP) model are compared to numerical results obtained with the exponential form of the Phan-Thien Tanner (PTT-a) and the Giesekus model and to experimental data of velocities and stresses. These models are known to be well capable of predicting all characteristic features encountered experimentally. Curiously, the eXtended Pom-Pom mode, formulated with the same non-affine or irreversible stretch dynamics as the original Pom-Pom model, encounters convergence problems using the DEVSS/DG method. A slight modification of the stretch dynamics such that it becomes consistent with other viscoelastic models and in agreement with a modification of the stretch dynamics based on non-equilibrium thermodynamics by Van Meerveld [J. Non-Newtonian Fluid Mech. 108 (2002) 291] gives a more numerical stable behaviour and steady state could be reached. From this it is clear that physical and numerical issues still play a mixed role in numerical viscoelastic flow problems. (C) 2004 Elsevier B.V. All rights reserved.