A posteriori error estimates for finite element approximation of unsteady incompressible stochastic navier-stokes equations

In this paper, we consider the unsteady incompressible stochastic Navier-Stokes equations containing a noise part. The purpose of this paper is to derive a posteriori error estimates for the finite element approximation of stochastic equations applied the weighted Clement-type interpolator. We obtain the posteriori error upper and lower bounds for the semidicretization scheme and the full backward Euler discretization scheme.