In this paper, we analyze Galerkin approximations for stochastic evolution
equations driven by an additive Gaussian noise which is temporally white and
spatially fractional with Hurst index less than or equal to 1/2. First we
regularize the noise by the Wong-Zakai approximation and obtain its optimal
order of convergence. Then we apply the Galerkin method to discretize the
stochastic evolution equations with regularized noises. Optimal error estimates
are obtained for the Galerkin approximations. In particular, our error
estimates remove an infinitesimal factor which appears in the error estimates
of various numerical methods for stochastic evolution equations in existing
literatures.Comment: 32 page
