Time-discretization of stochastic 2-D Navier--Stokes equations with a penalty-projection method
Provides theoretical convergence guarantees for a numerical scheme applied to stochastic Navier-Stokes equations, which is relevant for computational fluid dynamics researchers.
The authors analyze a time-discretization of stochastic 2-D Navier-Stokes equations using a penalty-projection method, deriving convergence rates of order 1/4 in probability for velocity and pressure, and strong convergence via the law of total probability.
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.