We consider overlap splines that are defined by connecting the patches of piecewise functions via common values at given finite sets of nodes, without using any partitions of the computational domain. It is shown that some classical finite difference methods may be interpreted as collocation with overlap splines. Moreover, several versions of the meshless finite difference methods, such as the RBF-FD method, are equivalent to the collocation or discrete least squares with appropriately chosen spaces of overlap splines.

翻译：我们研究重叠样条，其通过给定有限节点集合上的公共值连接分段函数补片来定义，无需使用计算域的任何划分。研究表明，若干经典有限差分方法可被解释为重叠样条配置法。此外，多种无网格有限差分方法（如RBF-FD方法）等价于在适当选取的重叠样条空间上进行的配置法或离散最小二乘法。