CONVERGENCE OF FLUX-SPLITTING FINITE VOLUME SCHEMES FOR HYPERBOLIC SCALAR CONSERVATION LAWS WITH A MULTIPLICATIVE STOCHASTIC PERTURBATION

摘要

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 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.