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


Author: Mireille Bossy
Journal: Math. Comp. 73 (2004), 777-812
MSC (2000): Primary 65C35, 65M15, 60H10, 60K35
DOI: https://doi.org/10.1090/S0025-5718-03-01551-5
Published electronically: June 18, 2003
MathSciNet review: 2031406
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Mireille Bossy
Affiliation: INRIA, 2004 Route des Lucioles, B.P. 93, 06902 Sophia-Antipolis Cedex, France
Email: Mireille.Bossy@sophia.inria.fr

DOI: https://doi.org/10.1090/S0025-5718-03-01551-5
Keywords: Stochastic particle method, viscous scalar conservation laws, Euler discretization scheme, weak convergence rate
Received by editor(s): April 5, 2001
Received by editor(s) in revised form: July 30, 2002
Published electronically: June 18, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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