On the convergence of a full discretization scheme for the stochastic Navier-Stokes equations

We mainly investigate the error approximation of stochastic Navier-Stokes equations driven by white noise. Herein the discretization about space is studied by finite element method, and in time it holds the backward Euler scheme. To obtain the optimal error estimations, the main error is divided into three parts. The proofs of the first two parts are based on the corresponding deterministic case. The third part which contains stochastic error is researched by the relevant norms and integrals.