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.

翻译：本文致力于基于含角动量旋转项的Gross-Pitaevskii方程，构建并分析用于计算旋转玻色-爱因斯坦凝聚体动力学的结构保持Galerkin方法。由于旋转项的存在，构建能同时保持质量和能量的有限元方法仍是一个未解决的问题，特别是在非协调有限元框架下。与现有研究相比，本文提供了完整的收敛性分析，全面论证了该方法的最优收敛性及高阶收敛特性。最后，通过大量数值结果验证了旋转玻色-爱因斯坦凝聚体结构保持数值方法的理论分析，并借助一系列数值实验深入考察了量子化涡旋晶格的行为特征。