Author:
Breit Dominic,Dodgson Alan
Abstract
AbstractWe study stochastic Navier–Stokes equations in two dimensions with respect to periodic boundary conditions. The equations are perturbed by a nonlinear multiplicative stochastic forcing with linear growth (in the velocity) driven by a cylindrical Wiener process. We establish convergence rates for a finite-element based space-time approximation with respect to convergence in probability (where the error is measured in the $$L^\infty _tL^2_x\cap L^2_tW^{1,2}_x$$
L
t
∞
L
x
2
∩
L
t
2
W
x
1
,
2
-norm). Our main result provides linear convergence in space and convergence of order (almost) 1/2 in time. This improves earlier results from Carelli and Prohl (SIAM J Numer Anal 50(5):2467–2496, 2012) where the convergence rate in time is only (almost) 1/4. Our approach is based on a careful analysis of the pressure function using a stochastic pressure decomposition.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics
Cited by
22 articles.
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