Finite-volume approximation of the invariant measure of a viscous stochastic scalar conservation law

Abstract We study the numerical approximation of invariant measure a viscous scalar conservation law, one-dimensional and periodic in space variable stochastically forced with white-in-time but spatially correlated noise. The flux function is assumed to be locally Lipschitz continuous have at most polynomial growth. scheme we employ discretizes stochastic partial differential equation (SPDE) according finite-volume method split-step backward Euler time. As first result, prove well posedness as existence uniqueness an for both semidiscrete scheme. Our main result then convergence measures discrete approximations, time steps go zero, towards SPDE, respect second-order Wasserstein distance. investigate rates theoretically, case where globally small constant, numerically Burgers equation.