Strong rates of convergence of space-time discretization schemes for the 2D Navier-Stokes equations with additive noise

Abstract

We consider the strong solution of the 2D Navier-Stokes equations in a torus subject to an additive noise. We implement a fully implicit time numerical scheme and a finite element method in space. We prove that the rate of convergence of the schemes is $\eta \in [0,1/2)$ in time and 1 in space. Let us mention that the coefficient $\eta$ is equal to the time regularity of the solution with values in $\LL^2$. Our method relies on the existence of finite exponential moments for both the solution and its time approximation. Our main idea is to use a discrete Gronwall lemma for the error estimate without any localization.

arXiv commentarXiv admin note: text overlap with arXiv:2004.06932

References in corpus (4)

• Inviscid Large deviation principle and the 2D Navier Stokes equations with a free boundary condition
• Splitting up method for the 2D stochastic Navier-Stokes equations
• On strong $L^2$ convergence of time numerical schemes for the stochastic 2D Navier-Stokes equations
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Cited by in corpus (3)

• Speed of convergence of time Euler schemes for a stochastic 2D Boussinesq model
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• A splitting semi-implicit method for stochastic incompressible Euler equations on ${\mathbb{T}}^2$