Convergence of time-splitting approximations for degenerate convection–diffusion equations with a random source

Abstract

Abstract In this paper we propose a time-splitting method for degenerate convection–diffusion equations perturbed stochastically by white noise. This work generalizes previous results on splitting operator techniques for stochastic hyperbolic conservation laws for the degenerate parabolic case. The convergence in Llocp$\begin{array}{} \displaystyle L^p_{\rm loc} \end{array}$ of the time-splitting operator scheme to the unique weak entropy solution is proven. Moreover, we analyze the performance of the splitting approximation by computing its convergence rate and showing numerical simulations for some benchmark examples, including a fluid flow application in porous media.