  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.
