The weighted particle method for convection-diffusion equations. I. The case of an isotropic viscosity. II. The anisotropic case

A particle method for convection-diffusion equations based on the approximation of diffusion operators by integral operators and the use of a particle method to solve integro-differential equations previously described is presented and studied. The isotropic diffusion operators are dealt with first. Two approximation possibilities are obtained, depending on whether or not the integral operator is positive. An extension of the method to anisotropic diffusion operators follows. The consistency and the accuracy of the method require much more complex conditions on the cutoff functions than in the isotropic case. After detailing these conditions, several examples of cutoff functions which can be used for practical computations are given. A detailed error analysis is then performed. 24 refs