A Galerkin Radial Basis Function Method for Nonlocal Diffusion

We introduce a meshfree Galerkin method for solving nonlocal diffusion problems. Radial basis functions are used to construct an approximation scheme that requires only scattered nodes with no triangulation. A quadrature scheme specific to radial basis functions is implemented to produce a Galerkin radial basis function method that yields fast assembly of a sparse stiffness matrix. We provide numerical evidence for convergence rates using one and two dimensional nonlocal problems.