A meshless method based on Radial Basis Function (RBF) interpolation and direct collocation is used to systematically solve steady state heat conduction problems on several 2D domains with different boundary conditions. The point sets, or distributions, needed by the method have been generated using two techniques: a relaxed quadtree technique and a high quality, geometry dependent, technique. The resulting solutions are then compared to the corresponding analytical solutions; FEM (Finite Method) solutions have also been computed as reference. These tests showed good convergence properties (II or IV order) for many of the considered cases, with an error of the same order of magnitude of classical FEM solutions, while a limited number of cases showed fluctuating convergence curves. These features confirm that this numerical approach could be an effective technique in the numerical simulation of practical heat conduction problems.
