English

Nonconforming Finite Element Approximation and Energy Lower Bound Estimation for the Gross--Pitaevskii Energy Functional

Numerical Analysis 2026-05-25 v1 Numerical Analysis

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 EQ1rotEQ_1^{\mathrm{rot}} finite element. Furthermore, we proof that within the EQ1rotEQ_1^{\mathrm{rot}} 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}
}