The finite element method for the time-dependent gross-pitaevskii equation with angular momentum rotation

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Bose-Einstein condensate

finite element method

Gross-Pitaevskii equation

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