Skip to Main content Skip to Navigation
Journal articles

Splitting up method for the 2D stochastic Navier-Stokes equations

Abstract : In this paper, we deal with the convergence of an iterative scheme for the 2-D stochastic Navier-Stokes Equations on the torus suggested by the Lie-Trotter product formulas for stochastic differential equations of parabolic type. The stochastic system is split into two problems which are simpler for numerical computations. An estimate of the approximation error is given either with periodic boundary conditions. In particular, we prove that the strong speed of the convergence in probability is almost $1/2$. This is shown by means of an $L^2(\Omega,P)$ convergence localized on a set of arbitrary large probability. The assumptions on the diffusion coefficient depend on the fact that some multiple of the Laplace operator is present or not with the multiplicative stochastic term. Note that if one of the splitting steps only contains the stochastic integral, then the diffusion coefficient may not contain any gradient of the solution.
Document type :
Journal articles
Complete list of metadatas

Cited literature [23 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00864579
Contributor : Annie Millet <>
Submitted on : Thursday, February 27, 2014 - 5:43:45 AM
Last modification on : Tuesday, May 26, 2020 - 5:20:06 PM
Document(s) archivé(s) le : Tuesday, May 27, 2014 - 10:51:38 AM

Files

Revised_Splitting_2DNS_HBZBAM....
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00864579, version 2
  • ARXIV : 1309.5633

Citation

Hakima Bessaih, Zdzislaw Brzezniak, Annie Millet. Splitting up method for the 2D stochastic Navier-Stokes equations. Stochastics and Partial Differential Equations: Analysis and Computations, Springer US, 2014, 2 (4), pp.433-470. ⟨hal-00864579v2⟩

Share

Metrics

Record views

528

Files downloads

290