On strong $L^2$ convergence of time numerical schemes for the stochastic 2D Navier-Stokes equations - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2019

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

Résumé

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.
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Dates et versions

hal-01684077 , version 1 (15-01-2018)
hal-01684077 , version 2 (10-07-2018)

Identifiants

  • HAL Id : hal-01684077 , version 2

Citer

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, 2019, 39 (4), pp.2135-2167. ⟨hal-01684077v2⟩
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