# Strong $L^2$ convergence of time numerical schemes for the stochastic two-dimensional Navier–Stokes equations

@article{Bessaih2018StrongC,
title={Strong \$L^2\$ convergence of time numerical schemes for the stochastic two-dimensional Navier–Stokes equations},
author={Hakima Bessaih and Annie Millet},
journal={IMA Journal of Numerical Analysis},
year={2018}
}
• Published 10 January 2018
• Mathematics, Computer Science
• IMA Journal of Numerical Analysis
We prove that some time discretization schemes for the two-dimensional Navier–Stokes equations on the torus subject to a random perturbation converge in $L^2(\varOmega )$. This refines previous results that established the convergence only 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 semiimplicit temporal…
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