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

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.

References in corpus (5)

• Mathematical theory and numerical methods for Bose-Einstein condensation
• Computational methods for the dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations
• An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates
• Dipolar Bose-Einstein Condensates in Weak Anisotropic Disorder
• Dipolar Bose-Einstein condensates in a PT-symmetric double-well potential