Structure-preserving finite element methods for computing dynamics of rotating Bose-Einstein condensate

TL;DR

This paper develops and analyzes structure-preserving finite element methods for simulating the dynamics of rotating Bose-Einstein condensates, ensuring mass and energy conservation with proven convergence properties.

Contribution

It introduces novel Galerkin finite element methods that preserve key physical structures for rotating BECs and provides a comprehensive convergence analysis.

Findings

Methods preserve mass and energy in simulations

Achieve optimal and high-order convergence

Numerical tests validate theoretical results

Abstract

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.