We consider the time-dependent Gross--Pitaevskii equation describing the dynamics of rotating Bose--Einstein condensates and its discretization with the finite element method. We analyze a mass conserving Crank--Nicolson-type discretization and prove corresponding a priori error estimates with respect to the maximum norm in time and the L²- and energy-norm in space. The estimates show that we obtain optimal convergence rates under the assumption of additional regularity for the solution to the Gross--Pitaevskii equation. We demonstrate the performance of the method in numerical experiments.
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Henning et al. (2017) studied this question.
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