Mesh resolution is a critical component in the development of cardiac digital twin models designed to replicate patient-specific electrophysiological behaviour. This parameter not only affects simulation performance, but also plays a pivotal role in accurately capturing arrhythmogenic mechanisms, such as ventricular re-entry, which is a key feature of life-threatening arrhythmias in heart diseases. In this study, we explore how different mesh resolutions influence the formation and stability of re-entry circuits using an healing infarcted region. Simulations are performed on a human-based biventricular model that includes a Purkinje network and an infarcted region with ionic remodeling by employing a high-performance GPU-based cardiac solver. Notably, we find that even when conduction velocities are adjusted to match across resolutions, the resulting re-entry onset differ, occurring around 4340ms, 3640ms and 5080ms, for 250um, 300um and 350um mesh resolutions, respectively. Execution times were 46.72hrs, 26.95hrs and 16.06hrs. These findings suggest the importance of mesh resolution choice in digital twin applications, particularly for arrhythmia risk assessment and personalized therapy planning that consider the Purkinje network.