Meshfree methods for solid mechanics have been in development since the early 1990’s. Initial motivations included alleviation of the burden of mesh creation and the desire to overcome the limitations of traditional mesh-based discretizations for extreme deformation applications. Here, the accuracy and robustness of both meshfree and mesh-based Lagrangian discretizations are compared using manufactured extreme deformation fields. For the meshfree discretizations, both moving least squares and maximum entropy are considered. Quantitative error and convergence results are presented for the best approximation in the \(H^1\) norm.

中文翻译：

---

使用制造的极端变形场的无网格和基于网格的拉格朗日近似的运动学比较

自1990年代初以来，一直在开发用于实体力学的无网格方法。最初的动机包括减轻网格创建的负担，并希望克服针对极端变形应用的传统基于网格的离散化方法的局限性。在这里，使用制造的极限变形场比较无网格和基于网格的拉格朗日离散化的准确性和鲁棒性。对于无网格离散化，要考虑移动最小二乘和最大熵。在\（H ^ 1 \）范数中给出了最佳近似的量化误差和收敛结果。