Orateur : Ming-Cheng Shiue
Établissement : National Chiao Tung University (Taiwan)
Dates : 2026-02-12 – 2026-02-12
Heures : 14:00 – 14:00
Lieu : Salle 0-3
Résumé :
Titre de la conférence : On the long-time stability of a class of second-order time-stepping schemes for the Navier-Stokes equationsThis talk explores the long-time stability of a class of second-order time-stepping schemes designed for the Navier-Stokes equations including BDF or SAV-BDF methods. The main results are to demonstrate that these time-stepping schemes enjoy long-time L^2 stability without requiring a small time step size. Additionally, for smoother initial data, these algorithms achieve long-time H^1-stability, also without imposing constraints on the time step size. Therefore, these results match the well-known theory for the Navier-Stokes equations and these numerical schemes are accurately capturing the asymptotic dynamical system to the Navier-Stokes equations.
This presentation investigates a novel class of second-order time-stepping methods for the Navier-Stokes equations, specifically incorporating BDF and SAV-BDF approaches. The key findings reveal that these schemes maintain long-time L² stability without the restriction of the time step size. Moreover, when the initial data is sufficiently smooth, the algorithms achieve enduring H¹ stability without requiring the smallness condition on the time step size. These results confirm that the numerical methods accurately reproduce the asymptotic behavior of the Navier-Stokes dynamics, in full agreement with the established theoretical framework.