Time-discretization of stochastic 2-D Navier–Stokes equations with a penalty-projection method

A time-discretization of the stochastic incompressible Navier–Stokes problem by penalty method is analyzed. Some error estimates are derived, combined, and eventually arrive at a speed of convergence in probability of order 1/4 of the main algorithm for the pair of variables velocity and pressure. Also, using the law of total probability, we obtain the strong convergence of the scheme for both variables.