Layer methods for stochastic Navier–Stokes equations using simplest characteristics
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...
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| Format: | Article |
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Elsevier
2016
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| Online Access: | https://eprints.nottingham.ac.uk/32272/ |
| _version_ | 1848794374698172416 |
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| author | Milstein, G.N. Tretyakov, M.V. |
| author_facet | Milstein, G.N. Tretyakov, M.V. |
| author_sort | Milstein, G.N. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:15:11Z |
| format | Article |
| id | nottingham-32272 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:15:11Z |
| publishDate | 2016 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-322722020-05-04T18:06:56Z https://eprints.nottingham.ac.uk/32272/ Layer methods for stochastic Navier–Stokes equations using simplest characteristics Milstein, G.N. Tretyakov, M.V. 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. Elsevier 2016-08-15 Article PeerReviewed Milstein, G.N. and Tretyakov, M.V. (2016) Layer methods for stochastic Navier–Stokes equations using simplest characteristics. Journal of Computational and Applied Mathematics, 302 . pp. 1-23. ISSN 1879-1778 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 http://www.sciencedirect.com/science/article/pii/S0377042716300310 doi:10.1016/j.cam.2016.01.051 doi:10.1016/j.cam.2016.01.051 |
| spellingShingle | 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 Milstein, G.N. Tretyakov, M.V. Layer methods for stochastic Navier–Stokes equations using simplest characteristics |
| title | Layer methods for stochastic Navier–Stokes equations using simplest characteristics |
| title_full | Layer methods for stochastic Navier–Stokes equations using simplest characteristics |
| title_fullStr | Layer methods for stochastic Navier–Stokes equations using simplest characteristics |
| title_full_unstemmed | Layer methods for stochastic Navier–Stokes equations using simplest characteristics |
| title_short | Layer methods for stochastic Navier–Stokes equations using simplest characteristics |
| title_sort | layer methods for stochastic navier–stokes equations using simplest characteristics |
| topic | 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 |
| url | https://eprints.nottingham.ac.uk/32272/ https://eprints.nottingham.ac.uk/32272/ https://eprints.nottingham.ac.uk/32272/ |