## Abstract

We study a finite-element based space-time discretisation for the 2D stochastic Navier–Stokes equations in a bounded domain supplemented with no-slip boundary conditions. We prove optimal convergence rates in the energy norm with respect to convergence in probability, that is convergence of order (almost) 1/2 in time and 1 in space. This was previously only known in the space-periodic case, where higher order energy estimates for any given (deterministic) time are available. In contrast to this, estimates in the Dirichlet-case are only known for a (possibly large) stopping time. We overcome this problem by introducing an approach based on discrete stopping times. This replaces the localised estimates (with respect to the sample space) from earlier contributions.

Original language | English |
---|---|

Journal | Foundations of Computational Mathematics |

Early online date | 26 Oct 2023 |

DOIs | |

Publication status | E-pub ahead of print - 26 Oct 2023 |

## Keywords

- Convergence rates
- Error analysis
- Space-time discretisation
- Stochastic Navier–Stokes equations

## ASJC Scopus subject areas

- Analysis
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics