We present an error bound for a least squares version of the kernel based meshless finite difference method for elliptic differential equations on smooth compact manifolds of arbitrary dimension without boundary. In particular, we obtain sufficient conditions for the convergence of this method. Numerical examples are provided for the equation $-\Delta_\mathcal{M} u + u = f$ on the 2- and 3-spheres, where $\Delta_\mathcal{M}$ is the Laplace-Beltrami operator.

翻译：我们提出一个最小方块的错误, 以最小方块为最小方块, 内核基于无网格的有限差分法, 用于无边界的任意尺寸平滑的紧凑式紧凑方块的椭圆差分方程式, 特别是, 我们为该方法的趋同获得足够的条件 。 为公式 $-\ Delta\\\ mathcal{M} 提供数字示例, 公式 $- delta\ mathcal{M} = f$- serphes, 以 $\ Delta\\ mathcal{M} 为Laplace- Beltrami 操作员 。