Optimal Rate of Convergence of a Stochastic Particle Method to Solutions of 1D Viscous Scalar Conservation Law Equations

The aim of this work is to present the analysis of the rate of convergence of a stochastic particle method for 1D viscous scalar conservation law equations. The convergence rate result is $\mathcal O(\D t + 1/\sqrt{N})$, where $N$ is the number of numerical particles and $\D t$ is the time step of the first order Euler scheme applied to the dynamic of the interacting particles.