  In this paper, we deal with the convergence of an iterative scheme for the
2-D stochastic Navier-Stokes Equations on the torus suggested by the
Lie-Trotter product formulas for stochastic differential equations of parabolic
type. The stochastic system is split into two problems which are simpler for
numerical computations. An estimate of the approximation error is given either
with periodic boundary conditions. In particular, we prove that the strong
speed of the convergence in probability is almost $1/2$. This is shown by means
of an $L^2(\Omega,P)$ convergence localized on a set of arbitrary large
probability. The assumptions on the diffusion coefficient depend on the fact
that some multiple of the Laplace operator is present or not with the
multiplicative stochastic term. Note that if one of the splitting steps only
contains the stochastic integral, then the diffusion coefficient may not
contain any gradient of the solution.
