Long time stability of a classical efficient scheme for two dimensional\n Navier-Stokes equations

2011/05/22 by Sigal Gottlieb, Gottlieb, Sigal, Florentina Tone +7 · 2 citations
Engineering · Mathematics · #37L40 #65M12 #65M70 #76D06 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Numerical Analysis (math.NA) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1105.4349

openalex publication_date 2011/05/22 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Gevrey class regularity for the solutions of the Navier-Stokes equations

Cited by

• Long-time stability and convergence analysis of an IMEX BDF3 scheme for 2-D incompressible Navier-Stokes equation
• Long-time stability analysis of an explicit exponential Runge-Kutta scheme for Cahn-Hilliard equations

Related

• Long time stability of a classical efficient scheme for an incompressible two-phase flow model
• An efficient second order in time scheme for approximating long time statistical properties of the two dimensional Navier-Stokes equations
• Unconditional long-time stability of a velocity-vorticity method for the\n 2D Navier-Stokes equations
• Long-time stable SAV-BDF2 numerical schemes for the forced Navier-Stokes equations
• Long-time stability and convergence analysis of an IMEX BDF3 scheme for 2-D incompressible Navier-Stokes equation