Layer methods for stochastic Navier-Stokes equations using simplest characteristics

DOI10.1016/j.cam.2016.01.051zbMath1334.65016OpenAlexW2253000656MaRDI QIDQ268290

M. V. Tretyakov, Grigori N. Milstein

Publication date: 14 April 2016

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2016.01.051

zbMATH Keywords

Navier-Stokes equationsstochastic partial differential equationsconditional Feynman-Kac formulaHelmholtz-Hodge-Leray decompositionOseen-Stokes equationsweak approximation of stochastic differential equations and layer methods

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

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Cites Work

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• Splitting up method for the 2D stochastic Navier-Stokes equations
• Kolmogorov equations for stochastic PDEs.
• Solving the Dirichlet problem for Navier-Stokes equations by probabilistic approach
• Characteristics of degenerate second-order parabolic Ito equations
• A note on Euler's approximations
• Backward doubly stochastic differential equations and systems of quasilinear SPDEs
• On the splitting-up method and stochastic partial differential equations
• An approximation method for Navier-Stokes equations based on probabilistic approach.
• Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing
• Global \(L_2\)-solutions of stochastic Navier-Stokes equations
• Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics
• Vorticity and Incompressible Flow
• Probabilistic Methods for the Incompressible Navier–Stokes Equations With Space Periodic Conditions
• Semigroup Splitting and Cubature Approximations for the Stochastic Navier–Stokes Equations
• An Introduction to 3D Stochastic Fluid Dynamics
• Solving parabolic stochastic partial differential equations via averaging over characteristics
• The probability approach to numerical solution of nonlinear parabolic equations
• Discretization of forward–backward stochastic differential equations and related quasi-linear parabolic equations
• Malliavin calculus for the stochastic 2D Navier—Stokes equation
• Monte Carlo methods for backward equations in nonlinear filtering
• Stochastic partial differential equations and filtering of diffusion processes
• Stationary solutions of nonlinear stochastic evolution equations¹
• Numerical solution of quasilinear parabolic equations and backward stochastic differential equations
• Stochastic Navier--Stokes Equations for Turbulent Flows
• On the Cauchy Problem for Stochastic Stokes Equations
• Rates of Convergence for Discretizations of the Stochastic Incompressible Navier--Stokes Equations
• A convergent finite-element-based discretization of the stochastic Landau-Lifshitz-Gilbert equation
• An interpolated stochastic algorithm for quasi-linear PDEs
• An Accelerated Splitting-up Method for Parabolic Equations
• Stochastic Equations in Infinite Dimensions