We give a rigorous error analysis for the full discretization of Gross-Pitaevskii
equations with rotation term. The model describes rotating Bose-Einstein condensates.
The spatial discretization uses a spectral method based on Laguerre-, Fourier-
and Hermite functions and the time integration is realized by high-order split-step
methods. We give a rigorous analysis of the discretization error and moreover
discuss practical aspects of adaptive step-size choice based on local error