The Finite Element Method for the Time-Dependent Gross--Pitaevskii Equation with Angular Momentum Rotation

Type: Article

Publication Date: 2017-01-01

Citations: 23

DOI: https://doi.org/10.1137/15m1009172

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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 $L^2$- 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.

Locations

  • SIAM Journal on Numerical Analysis - View
  • arXiv (Cornell University) - View - PDF
  • Chalmers Research (Chalmers University of Technology) - View - PDF

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