Layer methods for Navier-Stokes equations with additive noise

Abstract

We propose and study a number of layer methods for stochastic Navier-Stokes equations (SNSE) with spatial periodic boundary conditions and additive noise. The methods are constructed using conditional probabilistic representations of solutions to SNSE and exploiting ideas of the weak sense numerical integration of stochastic differential equations. We prove some convergence results for the proposed methods. Results of numerical experiments on two model problems are presented.