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