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

Abstract

Here, we study explicit flux-splitting finite volume discretizations of multi-dimensional nonlinear scalar conservation laws perturbed by a multiplicative noise with a given initial data inL2(Rd)L^{2}(\mathbb {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.