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Pré-Publication, Document De Travail Année : 2024

Finite volumes for the Gross-Pitaevskii equation

Résumé

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.
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Dates et versions

hal-04439060 , version 1 (05-02-2024)

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Quentin Chauleur. Finite volumes for the Gross-Pitaevskii equation. 2024. ⟨hal-04439060⟩
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