Issue |
ESAIM: M2AN
Volume 59, Number 1, January-February 2025
|
|
---|---|---|
Page(s) | 519 - 552 | |
DOI | https://doi.org/10.1051/m2an/2024067 | |
Published online | 16 January 2025 |
Structure-preserving finite element methods for computing dynamics of rotating Bose–Einstein condensates
1
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, P.R. China. Email: limeng@zzu.edu.cn
2
School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000, P.R. China
3
School of Science, Wuhan University of Technology, Wuhan 430070, P.R. China
* Corresponding author: wjunjun8888@163.com
Received:
31
January
2024
Accepted:
2
September
2024
This work is concerned with the construction and analysis of structure-preserving Galerkin methods for computing the dynamics of rotating Bose–Einstein condensate (BEC) based on the Gross–Pitaevskii equation with angular momentum rotation. Due to the presence of the rotation term, constructing finite element methods (FEMs) that preserve both mass and energy remains an unresolved issue, particularly in the context of nonconforming FEMs. Furthermore, in comparison to existing works, we provide a comprehensive convergence analysis, offering a thorough demonstration of the methods’ optimal and high-order convergence properties. Finally, extensive numerical results are presented to check the theoretical analysis of the structure-preserving numerical method for rotating BEC, and the quantized vortex lattice’s behavior is scrutinized through a series of numerical tests.
Mathematics Subject Classification: 35Q55 / 65M60 / 65M22
Key words: Rotating Bose–Einstein condensate / Gross–Pitaevskii equation / angular momentum rotation / structure-preserving / finite element methods
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.