  This paper is concerned with stochastic incompressible Navier-Stokes
equations with multiplicative noise in two dimensions with respect to periodic
boundary conditions. Based on the Helmholtz decomposition of the multiplicative
noise, semi-discrete and fully discrete time-stepping algorithms are proposed.
The convergence rates for mixed finite element methods based time-space
approximation with respect to convergence in probability for the velocity and
the pressure are obtained. Furthermore, with establishing some stability and
using the negative norm technique, the partial expectations of the $H^1$ and
$L^2$ norms of the velocity error are proved to converge optimally.
