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

We consider the strong solution of 2D Navier–Stokes equations in a torus subject to an additive noise. implement fully implicit time numerical scheme and finite element method space. prove that space-time rate convergence is “optimal” one, namely, [Formula: see text] 1 Let us mention coefficient equal regularity with values text]. Our relies on existence exponential moments for both its approximation. Unlike previous results, our main new idea use discrete Grönwall lemma error estimate without any localization.