Convergent finite element based discretization of a stochastic two‐phase flow model

Abstract

AbstractIn this paper, we propose a fully discrete finite element based discretization for the numerical approximation of the stochastic Allen‐Cahn‐Navier‐Stokes system on a bounded polygonal domain of , . We prove that the proposed numerical scheme is unconditionally solvable, has finite energies and constructs weak martingale solutions of the stochastic Allen‐Cahn‐Navier‐Stokes system when the discretisation step (both in time and in space) tends to zero.