Layer methods for stochastic Navier–Stokes equations using simplest characteristics

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摘要

We propose and study a layer method for stochastic Navier–Stokes equations (SNSE) with spatial periodic boundary conditions and additive noise. The method is 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 method including its first mean-square order. Results of numerical experiments on two model problems are presented.

论文关键词：65C30,60H15,60H35,Navier–Stokes equations,Oseen–Stokes equations,Helmholtz–Hodge–Leray decomposition,Stochastic partial differential equations,Conditional Feynman–Kac formula,Weak approximation of stochastic differential equations and layer methods

论文评审过程：Received 22 April 2015, Revised 28 January 2016, Available online 10 February 2016, Version of Record 26 February 2016.

论文官网地址：https://doi.org/10.1016/j.cam.2016.01.051