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

Abstract

In 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 ℝ 𝑑 , 𝑑 = 2, 3. 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.