Strong rates of convergence of space-time discretization schemes for the 2D Navier–Stokes equations with additive noise-Reference-Cited by-同舟云学术

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

Published:2022-01-26 Issue:02 Volume:22 Page:
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

Bessaih Hakima¹^ORCID,Millet Annie²³

Affiliation:

1. Florida International University, Mathematics and Statistics Department, 11200 SW 8th Street, Miami, FL 33199, USA

2. SAMM, EA 4543, Université Paris 1 Panthéon Sorbonne, 90 Rue de Tolbiac, F-75634 Paris Cedex, France

3. Université de Paris and Sorbonne Université, CNRS, Laboratoire de Probabilités, Statistique et Modélisation, F-75013 Paris, France

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 space-time rate of convergence is the “optimal” one, namely, [Formula: see text] in time and 1 in space. Let us mention that the coefficient [Formula: see text] is equal to the time regularity of the solution with values in [Formula: see text]. Our method relies on the existence of finite exponential moments for both the solution and its time approximation. Unlike previous results, our main new idea is the use of a discrete Grönwall lemma for the error estimate without any localization.

Funder

Simons Foundation

Publisher

World Scientific Pub Co Pte Ltd

Subject

Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219493722400056

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