We investigate the long-time behavior of the following efficient second order in time scheme for the 2D Navier-Stokes equations in a periodic box: The scheme is a combination of a 2nd-order in time backward-differentiation and a particular explicit Adams-Bashforth treatment of the advection term. Therefore, only a linear constant coefficient Poisson solver is needed at each time step. We prove uniform in time bounds on this scheme in L 2, H per1 and H per2 provided that the time-step is sufficiently small. These time uniform estimates further lead to the convergence of long-time statistics (stationary statistical properties) of the scheme to that of the NSE itself at vanishing time-step. © 2012 Springer-Verlag.
X. Wang, "An Efficient Second Order in Time Scheme for Approximating Long Time Statistical Properties of the Two Dimensional Navier-Stokes Equations," Numerische Mathematik, vol. 121, no. 4, pp. 753 - 779, Springer, Aug 2012.
The definitive version is available at https://doi.org/10.1007/s00211-012-0450-3
Mathematics and Statistics
International Standard Serial Number (ISSN)
Article - Journal
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01 Aug 2012