Finite volumes for the Gross-Pitaevskii equation
Quentin Chauleur
Published: 2024/2/6
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.