Convergence rates for the numerical approximation of the 2D stochastic Navier-Stokes equations

@article{Breit2021ConvergenceRF,
  title={Convergence rates for the numerical approximation of the 2D stochastic Navier-Stokes equations},
  author={Dominic Breit and Alan Dodgson},
  journal={Numerische Mathematik},
  year={2021},
  volume={147},
  pages={553-578}
}
We 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 measure in the $L^\infty_tL^2_x\cap L^2_tW^{1,2}_x$-norm). Our main result provides linear… 
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