The understanding of the magnetization dynamics plays an essential role in the design of many technological applications, e.g., magnetic sensors, actuators, and storage devices. In this talk, we discuss the numerical analysis of the Landau-Lifshitz-Gilbert (LLG) equation, a well-accepted model to describe the magnetization dynamics in ferromagnetic materials. The numerical approximation of this nonlinear parabolic PDE poses several challenges (e.g., nonlinearities, constraints, structure that needs to be preserved). In this talk, we present a structure-preserving numerical scheme, based on lowest-order finite elements in space, that is proven to be convergent towards a weak solution of the problem.