Convergence of flux-splitting finite volume schemes for hyperbolic scalar conservation laws with a multiplicative stochastic perturbation

Caroline Bauzet (1) , Julia Charrier (1) , Thierry Gallouët (1)

1 I2M - Institut de Mathématiques de Marseille

We study here explicit flux-splitting finite volume discretizations of multi-dimensional nonlinear scalar conservation laws perturbed by a multiplicative noise with a given initial data in $L^{2}(\R^d)$. Under a stability condition on the time step, we prove 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; flux-splitting scheme

Domaines: Analyse numérique [math.NA]

Caroline Bauzet, Julia Charrier, Thierry Gallouët. Convergence of flux-splitting finite volume schemes for hyperbolic scalar conservation laws with a multiplicative stochastic perturbation. Mathematics of Computation, 2016, ⟨10.1090/mcom/3084⟩. ⟨hal-00958427v2⟩