Convergence of monotone finite volume schemes for hyperbolic scalar conservation laws with multiplicative noise

Caroline Bauzet (1) , J. Charrier (1) , T. Gallouët (1)

1 I2M - Institut de Mathématiques de Marseille

We study here the discretization by monotone finite volume schemes of multi-dimensional nonlinear scalar conservation laws forced by a multiplicative noise with a time and space dependent flux-function and a given initial data in $L^{2}(\R^d)$. After establishing the well-posedness theory for solutions of such kind of stochastic problems, we prove under a stability condition on the time step the convergence of the finite volume approximation towards the unique stochastic entropy solution of the equation.

Mots clés: Stochastic PDE; first-order hyperbolic equation; multiplicative noise; finite volume method; monotone scheme; Godunov scheme; Kruzhkov smooth entropy

Domaines: Analyse numérique [math.NA]

Caroline Bauzet, J. Charrier, T. Gallouët. Convergence of monotone finite volume schemes for hyperbolic scalar conservation laws with multiplicative noise. Stochastics and Partial Differential Equations: Analysis and Computations, 2016, 4 (1), pp.150-223. ⟨10.1007/s40072-015-0052-z⟩. ⟨hal-01061019v3⟩