The Finite Element Method for the time-dependent Gross-Pitaevskii equation with angular momentum rotation

2015/02/17 by Henning, Patrick, Målqvist, Axel
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1502.05025

Abstract

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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