Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash 96 tok/s
Gemini 2.5 Pro 49 tok/s Pro
GPT-5 Medium 24 tok/s
GPT-5 High 36 tok/s Pro
GPT-4o 102 tok/s
GPT OSS 120B 434 tok/s Pro
Kimi K2 198 tok/s Pro
2000 character limit reached

Long time stability of a classical efficient scheme for two dimensional Navier-Stokes equations (1105.4349v1)

Published 22 May 2011 in math.NA and math.AP

Abstract: We prove that a popular classical implicit-explicit scheme for the 2D incompressible Navier--Stokes equations that treats the viscous term implicitly while the nonlinear advection term explicitly is long time stable provided that the time step is sufficiently small in the case with periodic boundary conditions. The long time stability in the $L2$ and $H1$ norms further leads to the convergence of the global attractors and invariant measures of the scheme to those of the NSE itself at vanishing time step. Both semi-discrete in time and fully discrete schemes with either Galerkin Fourier spectral or collocation Fourier spectral methods are considered.

List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

Summary

We haven't generated a summary for this paper yet.

Dice Question Streamline Icon: https://streamlinehq.com

Follow-up Questions

We haven't generated follow-up questions for this paper yet.