In the past two decades or so, stochastic computing has been a very active research field in scientific computing and numerical analysis. Much of the effort of stochastic computing has been focused on efficient numerical methods for stochastic partial differential equations.

In this talk I will talk about finite element approximations of steady state stochastic partial differential equations (SPDEs) with white noise perturbations. The noises are approximated through both the Wong-Zakai method and spectral methods. If time permitted, I will also mention numerical methods for evolutional SPDEs driven by fractional Brown motions.