TY - JOUR T1 - The Finite Element Method of a Euler Scheme for Stochastic Navier-Stokes Equations Involving the Turbulent Component JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 727 EP - 744 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/592.html KW - stochastic Navier-Stokes equations, finite element method, discrete scheme, and error estimation. AB -

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.