The Finite Element Method of a Euler Scheme for Stochastic Navier-Stokes Equations Involving the Turbulent Component

Abstract

In this paper we study the finite element approximation for stochastic Navier-Stokes equations including a turbulent part. The discretization for space is derived by finite element method, and we use the backward Euler scheme in time discretization. We apply the generalized $L_2$-projection operator to approximate the noise term. Under suitable assumptions, strong convergence error estimations with respect to the fully discrete scheme are well proved.