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arXiv · 2605.23334

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

Chen Zhang·Heyan Zhu·Wenbin Chen
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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 $EQ_1^{\mathrm{rot}}$ finite element. Furthermore, we proof that within the $EQ_1^{\mathrm{rot}}$ 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.

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Chen Zhang, Heyan Zhu, Wenbin Chen. 2026-05-22. Nonconforming Finite Element Approximation and Energy Lower Bound Estimation for the Gross--Pitaevskii Energy Functional. https://arxiv.org/abs/2605.23334

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