  Recently, we constructed a class of nonlocal Poisson model on manifold under
Dirichlet boundary with global $\mathcal{O}(\delta^2)$ truncation error to its
local counterpart, where $\delta$ denotes the nonlocal horizon parameter. In
this paper, the well-posedness of such manifold model is studied. We utilize
Poincare inequality to control the lower order terms along the
$2\delta$-boundary layer in the weak formulation of model. The second order
localization rate of model is attained by combining the well-posedness argument
and the truncation error analysis. Such rate is currently optimal among all
nonlocal models. Besides, we implement the point integral method(PIM) to our
nonlocal model through 2 specific numerical examples to illustrate the
quadratic rate of convergence on the other side.
