  We introduce a meshless method for solving both continuous and discrete
variational formulations of a volume constrained, nonlocal diffusion problem.
We use the discrete solution to approximate the continuous solution. Our method
is nonconforming and uses a localized Lagrange basis that is constructed out of
radial basis functions. By verifying that certain inf-sup conditions hold, we
demonstrate that both the continuous and discrete problems are well-posed, and
also present numerical and theoretical results for the convergence behavior of
the method. The stiffness matrix is assembled by a special quadrature routine
unique to the localized basis. Combining the quadrature method with the
localized basis produces a well-conditioned, symmetric matrix. This then is
used to find the discretized solution.
