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}
}
  • H. Bessaih, A. Millet
  • 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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Space-time Euler discretization schemes for the stochastic 2D Navier-Stokes equations
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We prove that the implicit time Euler scheme coupled with finite elements space discretization for the 2D Navier-Stokes equations on the torus subject to a random perturbation converges in…
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