In this study, we build a complete model for the melted polymer during the injection phase. We use the in-house finite-elements solver XNS to simulate the polymer and air flows. To distinguish between the air and the polymer phase, we use the level-set approach, which captures the interface of the two-phase flow. For the polymer characterization, we use the non-Newtonian Cross-WLF rheology model, and to extend the model to semi-crystalline polymers, we use the Nakamura and the Hoffman-Lauritzen models, which describe the crystallization process. For higher computational efficiency, the space-time method is. This method permits the refinement of the time-stepping locally in areas of interest, such as the moving interface. The results and performance of the injection molding simulation and the advantages of using the space-time method for these simulations are analyzed.