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