Finite-element-based discretizations of the incompressible Navier–Stokes equations with multiplicative random forcing

@article{Brzeniak2013FiniteelementbasedDO,
  title={Finite-element-based discretizations of the incompressible Navier–Stokes equations with multiplicative random forcing},
  author={Zdzisław Brzeźniak and Erich Carelli and Andreas Prohl},
  journal={Ima Journal of Numerical Analysis},
  year={2013},
  volume={33},
  pages={771-824}
}
We study finite element based space-time discretisations of the incompressible Navier-Stokes equations with noise. In three dimensions, sequences of numerical solutions construct weak martingale solutions for vanishing discretisation parameters. In the two dimensional case, numerical solutions converge to the unique strong solution. 
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