Free access article

ESAIM: Proc., 2005, Vol. 15, pp. 18-57
DOI: 10.1051/proc:2005019

Some stochastic particle methods for nonlinear parabolic PDEs

Mireille Bossy

INRIA 2004 Route des Lucioles, B.P. 93 06902 Sophia-Antipolis Cedex France

Mireille.Bossy@sophia.inria.fr

Abstract
We introduce, on some examples, the main tools to analyze the convergence rate of stochastic particle methods for the numerical approximation of some nonlinear parabolic PDEs. We treat the case of Lipschitz coefficients as well as the case of viscous scalar conservation laws. We also discuss some particular aspects like the case of a bounded spatial domain or the use of a Romberg extrapolation as a speed up procedure.

Résumé
On introduit, sur certains exemples, les outils principaux pour l'analyse du taux de convergence des méthodes particulaires stochastiques pour l'approximation numérique de quelques EDPs paraboliques non-linéaires. On traite le cas de coefficients lipschitziens, ainsi que le cas des lois de conservation scalaires. On discute quelques aspects particuliers comme le cas d'un domaine spatial borné ou l'utilisation de l'extrapolation de Romberg comme procédé d'accélération.

© EDP Sciences, ESAIM 2005

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