Title :

Finite volumes for the Gross-Pitaevskii equation

Author(s) :

Chauleur, Quentin [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Systèmes de particules et systèmes dynamiques [Paradyse]

English keyword(s) :

Nonlinear Schrödinger equations
Lie-Trotter splitting
Finite-volume method
Convergence analysis
Quantum turbulence

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM) - UMR 8523

Source :

Harvested from HAL