Layer methods for stochastic Navier–Stokes equations using simplest characteristics

Milstein, G.N.; Tretyakov, M.V.

Abstract

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.

Citation

Milstein, G., & Tretyakov, M. (2016). Layer methods for stochastic Navier–Stokes equations using simplest characteristics. Journal of Computational and Applied Mathematics, 302, https://doi.org/10.1016/j.cam.2016.01.051

• Journal Article Type: Article
• Acceptance Date: Jan 28, 2016
• Online Publication Date: Feb 10, 2016
• Publication Date: Aug 15, 2016
• Deposit Date: Mar 14, 2016
• Publicly Available Date: Mar 14, 2016
• Journal: Journal of Computational and Applied Mathematics
• Print ISSN: 0377-0427
• Electronic ISSN: 1879-1778
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 302
• DOI: https://doi.org/10.1016/j.cam.2016.01.051
• Keywords: 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 Mathods
• Public URL: https://nottingham-repository.worktribe.com/output/805583
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0377042716300310
• Contract Date: Mar 14, 2016