Localized collocation methods based on radial basis functions (RBFs) for elliptic problems appear to be non-robust in the presence of Neumann boundary conditions. In this paper we overcome this issue by formulating the RBF-generated finite difference method in a discrete least-squares setting instead. This allows us to prove high-order convergence under node refinement and to numerically verify that the least-squares formulation is more accurate and robust than the collocation formulation. The implementation effort for the modified algorithm is comparable to that for the collocation method.

翻译：在新曼边界条件下,基于对椭圆形问题的辐射基功能(RBFs)的本地化合用方法似乎是非沸腾的,在本文件中,我们通过在离散的最小平方设置中制定RBF产生的有限差异法来解决这个问题。这使我们能够证明在节点改进下高度级趋同,并从数字上核实最小平方的配方比合用方配方的配方更准确、更稳健。修改后算法的实施努力与合用法相似。