Type: Article
Publication Date: 2017-01-01
Citations: 23
DOI: https://doi.org/10.1137/15m1009172
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 $L^2$- 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.