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.

翻译：我们研究了二维和三维空间中带时变势的 Gross-Pitaevskii 方程的 Voronoi 有限体积格式近似。在时间积分中采用显式分裂格式，同时空间上使用两点通量近似格式。我们基于离散一致 Sobolev 不等式严格分析了误差界，并证明了波函数的伪涡度收敛性。最后，通过数值模拟验证了理论结果。