Instabilities in polymer processing limit production rates and may influence to some degree the optical or mechanical properties of the final product. One prominent example is the fountain flow instability, which takes place during the mold filling stage of an injection molding process. It has been shown experimentally that these instabilities manifest themselves in the form of a periodic oscillation of the flow front stagnation point between the two walls of the mold channels. The onset of instability is determined by a critical Weissenberg number, at which perturbations to the steady flow are amplified rather than damped. Different values have been predicted numerically in previous work, and . We use the finite element method (FEM) and a number of stabilization techniques for flows of convective (SUPG) and viscoelastic (DEVSS-G) nature to do a full non-linear, transient simulation of a branched polymer melt (XPP constitutive model) in a channel. We investigate both the onset and behavior of the fountain flow instability, with the focus on distinguishing the mechanisms that drive the instability, and their physical interpretation. Several numerical difficulties had to be overcome, like the treatment of the contact point where the polymer is deposited on the mold wall. A perturbation is applied to the symmetric steady state flow field. We analyze the stability of the system by observing the perturbation norm (how much the flow deviates from the steady state flow field). We can also predict for which Weissenberg number a perturbation grows, and for which it is damped. For high Weissenberg numbers, we observe a clear oscillating behavior of the flow field, as seen in experiments.