Convergence of the Finite Volume Method for scalar conservation laws with multiplicative noise: an approach by kinetic formulation

Sylvain Dotti (1) , Julien Vovelle (2)

1 CEMOI - Centre d'Économie et de Management de l'Océan Indien
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We prove the convergence of the explicit-in-time Finite Volume method with monotone fluxes for the approximation of scalar first-order conservation laws with multiplicative, compactly supported noise.

Mots clés: Finite Volume Method; kinetic formu- lation; kinetic formulation; stochastic scalar conservation law

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Probabilités [math.PR]

Sylvain Dotti, Julien Vovelle. Convergence of the Finite Volume Method for scalar conservation laws with multiplicative noise: an approach by kinetic formulation. Stochastics and Partial Differential Equations: Analysis and Computations, In press. ⟨hal-01391073v4⟩