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Numerical analysis of 2D Navier--Stokes equations with additive stochastic forcing

Numerical Analysis 2022-03-23 v2 Numerical Analysis Analysis of PDEs Probability

Abstract

We propose and study a temporal, and spatio-temporal discretisation of the 2D stochastic Navier--Stokes equations in bounded domains supplemented with no-slip boundary conditions. Considering additive noise, we base its construction on the related nonlinear random PDE, which is solved by a transform of the solution of the stochastic Navier--Stokes equations. We show strong rate (up to) 11 in probability for a corresponding discretisation in space and time (and space-time). Convergence of order (up to) 1 in time was previously only known for linear SPDEs.

Keywords

Cite

@article{arxiv.2110.05894,
  title  = {Numerical analysis of 2D Navier--Stokes equations with additive stochastic forcing},
  author = {Dominic Breit and Andreas Prohl},
  journal= {arXiv preprint arXiv:2110.05894},
  year   = {2022}
}