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：我们针对光滑紧致无边界流形上的椭圆型微分方程，给出了基于核的无网格有限差分法最小二乘版本的误差界。特别地，我们得到了该方法收敛的充分条件。针对方程 $-\Delta_\mathcal{M} u + u = f$（其中 $\Delta_\mathcal{M}$ 为 Laplace-Beltrami 算子）在二维和三维球面上的情形，提供了数值算例。