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

Abstract

We prove that some discretization schemes for the 2D Navier-Stokes equations 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 NS 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.

References in corpus (1)

• Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations

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• Space-time Euler discretization schemes for the stochastic 2D Navier-Stokes equations
• Speed of convergence of time Euler schemes for a stochastic 2D Boussinesq model
• Strong convergence for explicit space-time discrete numerical approximation for 2D stochastic Navier-Stokes equations
• Analysis of Chorin-Type Projection Methods for the Stochastic Stokes Equations with General Multiplicative Noises
• High moment and pathwise error estimates for fully discrete mixed finite element approximations of the Stochastic Stokes Equations with Multiplicative Noises
• Strong L2 convergence of time Euler schemes for stochastic 3D Brinkman-Forchheimer-Navier-Stokes equations
• A splitting semi-implicit method for stochastic incompressible Euler equations on ${\mathbb{T}}^2$