  We study the approximation by a Voronoi finite-volume scheme of the
Gross-Pitaevskii equation with time-dependent potential in two and three
dimensions. We perform an explicit splitting scheme for the time integration
alongside a two-point flux approximation scheme in space. We rigorously analyze
the error bounds relying on discrete uniform Sobolev inequalities. We also
prove the convergence of the pseudo-vorticity of the wave function. We finally
perform some numerical simulations to illustrate our theoretical results.
