Finite element simulations of high speed rotating devices suffers from numerical instabilities due to the presence of a dominant convection term in the magnetomotional partial differential equation. The problem is cured by a combined approach consisting of an artificial diffusion upwind technique and an adaptive mesh refinement. The local refinement of the mesh, based on the error estimation of intermediate solutions, results in an optimal distribution of the finite elements. The upwind scheme ensures the stability of these intermediate solutions. The braking torque of a high-speed rotating magnetic brake is examined. Applying this combined approach, accurate solutions are obtained with minimal computational efforts.