A convergence proof of three high-order deterministic particle methods for the convection-diffusion equation 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 formulas for kernels which satisfy these conditions to arbitrary order are presented.

Comm. Pure Appl. Math., 50 (1997), pp. 1235-1260.

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@article{Cortez1997,
        author = {Ricardo Cortez},
        title = {Convergence of high-order deterministic particle
                 methods for the convection-diffusion equation},
        journal = {Comm. Pure Appl. Math.},
        volume = {50},
        number = {L},
        year = {1997},
        pages = {1235--1260}
}