Space-Time Approximation of Local Strong Solutions to the 3D Stochastic Navier–Stokes Equations

Dominic Breit, Alan Dodgson

Research output: Contribution to journalArticlepeer-review

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 for the energy error with respect to convergence in probability, that is convergence of order (up to) 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.
Original languageEnglish
JournalComputational Methods in Applied Mathematics
Early online date8 Aug 2023
DOIs
Publication statusE-pub ahead of print - 8 Aug 2023

Keywords

  • Convergence Rates
  • Error Analysis
  • Local Strong Solutions
  • Space-Time Discretisation
  • Stochastic Navier-Stokes Equations

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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