Error estimates of finite element methods for fractional stochastic Navier-Stokes equations.

Based on the Itô's isometry and the properties of the solution operator defined by the Mittag-Leffler function, this paper gives a detailed numerical analysis of the finite element method for fractional stochastic Navier-Stokes equations driven by white noise. The discretization in space is derived by the finite element method and the time discretization is obtained by the backward Euler scheme. The noise is approximated by using the generalized -projection operator. Optimal strong convergence error estimates in the -norm are obtained.