Error analysis of finite element approximations of the stochastic Stokes equations

摘要

Numerical solutions of the stochastic Stokes equations driven by white noise perturbed forcing terms using finite element methods are considered. The discretization of the white noise and finite element approximation algorithms are studied. The rate of convergence of the finite element approximations is proved to be almost first order (h|ln h|) in two dimensions and one half order () in three dimensions. Numerical results using the algorithms developed are also presented.