发表机构
College of Oceanography, Hohai University; SKLMS, Academy of Mathematics and Systems Science, Chinese Academy of Science（河海大学海洋学院; 中国科学院数学与系统科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一个严格判据：变形网格有效当且仅当每个单元内雅可比行列式为正且边界保持，为广义拉格朗日与ALE方法提供逐单元验证方法。
AI 中文摘要
数学上证明了变形网格保持有效的充分条件是：在整个时间区间内，每个单元内的变形雅可比行列式保持为正，且边界在变形下保持不变。该结果为广义拉格朗日格式和任意拉格朗日-欧拉格式的用户提供了一种严格且逐单元检查网格有效性的方法。
英文摘要
It is mathematically proved that, for a grid under a boundary-preserving piecewise-smooth deformation, the positivity of the Jacobian determinant in each closed element is also a sufficient condition for the deformed grid to remain valid. Most of the proof is devoted to showing that the element-wise positivity of the Jacobian indeed induces a local isomorphism in the grid-deformation setting. This result provides users of ALE methods and of the generalized Lagrangian method with a clean answer: checking the Jacobian alone is enough to determine the validity of the deformed grid.
