Optimal rate of convergence of a stochastic particle method to solutions of 1D viscous scalar conservation laws

Bossy, Mireille

doi:10.1090/S0025-5718-03-01551-5

Optimal rate of convergence of a stochastic particle method to solutions of 1D viscous scalar conservation laws
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Math. Comp. 73 (2004), 777-812 Request permission

Abstract:

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

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