Finite volumes for the Gross-Pitaevskii equation
Numerical Analysis
2025-09-11 v2 Numerical Analysis
Abstract
We study the approximation by a semi-discrete finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two dimensions, performing a two-point flux approximation scheme in space. We rigorously analyze the error bounds relying on discrete uniform Sobolev inequalities. We finally perform some numerical simulations to investigate convergence error.
Keywords
Cite
@article{arxiv.2402.03821,
title = {Finite volumes for the Gross-Pitaevskii equation},
author = {Quentin Chauleur},
journal= {arXiv preprint arXiv:2402.03821},
year = {2025}
}