CONVERGENCE RATE FOR THE APPROXIMATION OF THE LIMIT LAW OF WEAKLY INTERACTING PARTICLES: APPLICATION TO THE BURGERS EQUATION
成果类型：
Article
署名作者：
Bossy, Mireille; Talay, Denis
署名单位：
Inria; Universite Cote d'Azur
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1996
页码：
818-861
关键词：
摘要：
In this paper we construct a stochastic particle method for the Burgers equation with a monotone initial condition; we prove that the convergence rate is O (1/root N + root Delta t. for the L-1 (R X Omega). norm of the error. To obtain that result, we link the PDE and the algorithm to a system of weakly interacting stochastic particles; the difficulty of the analysis comes from the discontinuity of the interaction kernel, which is equal to the Heaviside function. In a previous paper we showed how the algorithm and the result extend to the case of nonmonotone initial conditions for the Burgers equation. We also treated the case of nonlinear PDE's related to particle systems with Lipschitz interaction kernels. Our next objective is to adapt our methodology to the (more difficult) case of the two-dimensional inviscid Navier-Stokes equation.