English

Space-time approximation of local strong solutions to the 3D stochastic Navier-Stokes equations

Numerical Analysis 2023-02-28 v2 Numerical Analysis Analysis of PDEs Probability

Abstract

We consider the 3D stochastic Navier-Stokes equation on the torus. Our main result concerns the temporal and spatio-temporal discretisation of a local strong pathwise solution. We prove optimal convergence rates in for the energy error with respect to convergence in probability, that is convergence of order 1 in space and of order (up to) 1/2 in time. The result holds up to the possible blow-up of the (time-discrete) solution. Our approach is based on discrete stopping times for the (time-discrete) solution.

Keywords

Cite

@article{arxiv.2211.17011,
  title  = {Space-time approximation of local strong solutions to the 3D stochastic Navier-Stokes equations},
  author = {Dominic Breit and Alan Dodgson},
  journal= {arXiv preprint arXiv:2211.17011},
  year   = {2023}
}

Comments

We corrected some typos. arXiv admin note: text overlap with arXiv:2109.06495