Skip to Main content Skip to Navigation
Journal articles

On strong $L^2$ convergence of time numerical schemes for the stochastic 2D Navier-Stokes equations

Abstract : We prove that some time discretization schemes for the 2D Navier-Stokes equations on the torus subject to a random perturbation converge in $L^2(\Omega)$. This refines previous results which only established the convergence in probability of these numerical approximations. Using exponential moment estimates of the solution of the stochastic Navier-Stokes equations and convergence of a localized scheme, we can prove strong convergence of fully implicit and semi-implicit time Euler discretizations, and of a splitting scheme. The speed of the $L^2(\Omega)$-convergence depends on the diffusion coefficient and on the viscosity parameter.
Document type :
Journal articles
Complete list of metadatas

Cited literature [21 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01684077
Contributor : Annie Millet <>
Submitted on : Tuesday, July 10, 2018 - 2:50:03 PM
Last modification on : Friday, April 10, 2020 - 5:26:47 PM
Document(s) archivé(s) le : Thursday, October 11, 2018 - 12:36:47 PM

File

StrongL2_cv_Bessaih-Millet-Jul...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01684077, version 2

Citation

Hakima Bessaih, Annie Millet. On strong $L^2$ convergence of time numerical schemes for the stochastic 2D Navier-Stokes equations. IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2019, 39 (4), pp.2135-2167. ⟨hal-01684077v2⟩

Share

Metrics

Record views

75

Files downloads

182