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 can 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 overlap splines, for appropriately chosen patches.

翻译：本文研究重叠样条，此类样条通过给定有限节点集上的公共值连接分段函数片段而定义，无需对计算域进行任何划分。研究表明，若干经典有限差分方法可被解释为利用重叠样条进行配置（collocation）的过程。此外，对于适当选取的片段，多种无网格有限差分方法（如RBF-FD方法）等价于基于重叠样条的配置法或离散最小二乘法。