Abstract In this project, we study the rotating Bose–Einstein condensate (BEC) from a numerical perspective. Our primary focus is the ground state, i.e., the minimum-energy configuration, which is obtained by solving a constrained minimization problem of the Gross–Pitaevskii energy functional describing the condensate’s total energy. When the BEC is set into rotation, quantized vortices emerge. These vortices appear at a very small scale compared to the whole condensate, giving rise to significant numerical challenges. The main difficulty is the need for a very high mesh resolution as required by mesh-dependent methods, which directly translates into a high computational cost. Moreover, as the rotation increases, more vortices are formed, further increasing the demand for computational resources. The question we aim to answer is how vortex formation influences the finite element mesh resolution required when computing the ground state. For that, we consider the ε-scaled Gross–Pitaevskii energy in the Thomas–Fermi rapid rotation regime, where 0<ε<<1 . As ε → 0, the system enters a regime of rapid rotation, strong interactions and vortex rich states. In this setting, we derive error estimates in the H¹ scaled norm and corresponding mesh resolution conditions in respect to ε. So, our next goal is to verify both the error bounds and this resolution condition numerically. Beyond this work we are extending similar error estimates, both analytically and numerically, for the multi scaled Localized orthogonal decomposition method and then compare it with the standard finite element method. Main Supervisor: Anna Persson