Convergence of high-order deterministic particle methods for the convection-diffusion equation

A proof of high-order convergence of three deterministic particle methods for the convection-diffusion equation in two dimensions is presented. The methods are based on discretizations of an integro-differential equation in which an integral operator approximates the diffusion operator. The methods differ in the discretization of this operator. The conditions for convergence imposed on the kernel that defines the integral operator include moment conditions and a condition on the kernel's Fourier transform. Explicit formulae for kernels that satisfy these conditions to arbitrary order are presented. (C) 1997 John Wiley & Sons, Inc.