发表机构
Univ. Lille, CNRS, Inria, UMR 8524 - Laboratoire Paul Painlevé（里尔大学，法国国家科学研究中心，法国研究与计算机科学研究所，UMR 8524 - 保罗·庞莱韦实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对带角动量旋转的定常Gross-Pitaevskii方程，通过有限体积格式逼近其极小化子，证明了离散极小化子的收敛性及归一化梯度流的指数收敛性，并以数值模拟验证结果。
AI 中文摘要
我们研究带角动量旋转的定常Gross-Pitaevskii方程的有限体积格式逼近。在标准网格正则性假设下，我们证明当网格直径趋于0时，离散全局极小化子收敛到连续全局极小化子。此外，在离散能量的海森矩阵的谱间隙假设下，我们证明归一化连续梯度流的解以指数速度收敛到该离散极小化子。我们还表明，上述离散谱间隙假设可由连续情形的类似假设导出。我们通过数值模拟验证了理论结果，这些模拟拓宽了分析的范围。
英文摘要
We study the approximation by a finite volume scheme of the stationary Gross-Pitaevskii equation with angular momentum rotation. We prove that, under standard mesh regularity assumptions, the discrete global minimizers converge to the continuous one as the mesh diameter tends to zero. Moreover, under a spectral gap assumption on the Hessian of the discrete energy, we prove that solutions to a normalized continuous gradient flow converges exponentially fast to such discrete minimizers. Additionally, we show that this previous discrete spectral gap assumption can be derived from similar hypotheses in the continuous setting. We support our theoretical results with numerical simulations, which broaden the scope of the analysis.
