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In this paper, we consider an energy-conserving continuous Galerkindiscretization of the Gross-Pitaevskii equation with a magnetic trappingpotential and a stirring potential for angular momentum rotation. Thediscretization is based on finite elements in space and time and allows forarbitrary polynomial orders. It was first analyzed in [O. Karakashian, C.Makridakis; SIAM J. Numer. Anal. 36(6):1779-1807, 1999] in the absence ofpotential terms and corresponding a priori error estimates were derived in 2D.In this work we revisit the approach in the generalized setting of theGross-Pitaevskii equation with rotation and we prove uniform $L^\infty$-boundsfor the corresponding numerical approximations in 2D and 3D without couplingconditions between the spatial mesh size and the time step size. With thisresult at hand, we are in particular able to extend the previous errorestimates to the 3D setting while avoiding artificial CFL conditions.

Uniform $L^\infty$-bounds for energy-conserving higher-order time integrators for the Gross-Pitaevskii equation with rotation