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arXiv · 2102.01162

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

Hakima Bessaih·Annie Millet
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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.

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Hakima Bessaih, Annie Millet. 2021-02-01. Strong rates of convergence of space-time discretization schemes for the 2D Navier-Stokes equations with additive noise. https://doi.org/10.1142/s0219493722400056

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