Finite volumes for the Gross-Pitaevskii equation
<|reference_start|>Finite volumes for the Gross-Pitaevskii equation: 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.<|reference_end|>
@article{chauleur2024finite,
    title={Finite volumes for the Gross-Pitaevskii equation},
    author={Quentin Chauleur (LPP, PhLAM, Paradyse)},
    journal={arXiv preprint arXiv:2402.03821},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.03821},
    primaryClass={math.NA cs.NA}
}