  This paper is concerned with numerical analysis of two fully discrete
Chorin-type projection methods for the stochastic Stokes equations with general
non-solenoidal multiplicative noise. The first scheme is the standard Chorin
scheme and the second one is a modified Chorin scheme which is designed by
employing the Helmholtz decomposition on the noise function at each time step
to produce a projected divergence-free noise and a "pseudo pressure" after
combining the original pressure and the curl-free part of the decomposition.
Optimal order rates of the convergence are proved for both velocity and
pressure approximations of these two (semi-discrete) Chorin schemes. It is
crucial to measure the errors in appropriate norms. The fully discrete finite
element methods are formulated by discretizing both semi-discrete Chorin
schemes in space by the standard finite element method. Suboptimal order error
estimates are derived for both fully discrete methods. It is proved that all
spatial error constants contain a growth factor $k^{-1/2}$, where $k$ denotes
the time step size, which explains the deteriorating performance of the
standard Chorin scheme when $k\to 0$ and the space mesh size is fixed as
observed earlier in the numerical tests of [9]. Numerical results are also
provided to guage the performance of the proposed numerical methods and to
validate the sharpness of the theoretical error estimates.
