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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| Veröffentlicht in: | Journal of computational and applied mathematics 2016-08, Vol.302, p.1-23 |
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| container_title | Journal of computational and applied mathematics |
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| creator | Milstein, G.N. Tretyakov, M.V. |
| 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. |
| doi_str_mv | 10.1016/j.cam.2016.01.051 |
| format | Article |
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| ispartof | Journal of computational and applied mathematics, 2016-08, Vol.302, p.1-23 |
| issn | 0377-0427 1879-1778 |
| language | eng |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; ScienceDirect Journals (5 years ago - present) |
| subjects | Conditional Feynman–Kac formula Convergence Differential equations Helmholtz–Hodge–Leray decomposition Mathematical analysis Mathematical models Navier-Stokes equations Oseen–Stokes equations Probability theory Representations Stochastic partial differential equations Stochasticity Weak approximation of stochastic differential equations and layer methods |
| title | Layer methods for stochastic Navier–Stokes equations using simplest characteristics |
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