A comparison of several numerical methods for the solution of the Convection-Diffusion Equation using the method of finite spheres

In this paper we compare several numerical methods for the solution of the convection-diffusion equation using the method of finite spheres; a truly meshfree numerical technique for the solution of boundary value problems. By conducting numerical inf-sup tests on a one-dimensional model problem it is found that a higher order derivative artificial diffusion (Ho DAD) method performs the best among the schemes tested. This method is then applied to the analysis of problems in two-dimensions.