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

02/01/2021

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by   Hakima Bessaih, et al.

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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 η∈[0,1/2) in time and 1 in space. Let us mention that the coefficient η is equal to the time regularity of the solution with values in ^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.