__A generalized finite difference method using CoatmÃ¨lec lattices__

Generalized finite difference methods require that a properly posed set of nodes exists around each node
in the mesh, so that the solution for the corresponding multivariate interpolation problem be unique. In
this paper we first show that the construction of these meshes can be computerized using a relatively
simple algorithm based on the concept of a CoatmÃ¨lec lattice. Then, we present a generalized finite
difference method which provides a numerical solution of a partial differential equation over an arbitrary
domain, using the generated meshes. The accuracy and mesh adaptivity of the method is evaluated using
elliptical equations in several domains.