Nonconforming Finite Element Approximation and Energy Lower Bound Estimation for the Gross--Pitaevskii Energy Functional
Abstract
The ground state of Bose--Einstein condensates can be described as the minimizer of the Gross--Pitaevskii energy functional subject to a mass conservation constraint. In this paper, we study the corresponding discrete optimization problem in nonconforming finite element spaces and establish a priori error estimates for the discrete ground state energy, the discrete eigenvalue, and the discrete ground state. Specifically, we derive explicit convergence rates for the a priori error in the particular case of the finite element. Furthermore, we proof that within the finite element framework, the discrete ground state energy provides a lower bound estimation to the exact energy. Finally, numerical experiments are presented to validate the theoretical analysis.
Keywords
Cite
@article{arxiv.2605.23334,
title = {Nonconforming Finite Element Approximation and Energy Lower Bound Estimation for the Gross--Pitaevskii Energy Functional},
author = {Chen Zhang and Heyan Zhu and Wenbin Chen},
journal= {arXiv preprint arXiv:2605.23334},
year = {2026}
}