Remarks on the approximation of the Navier-Stokes equations via the implicit Euler scheme

Michele Coti Zelati

doi:10.3934/cpaa.2013.12.2829

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2013, Volume 12, Issue 6: 2829-2838. Doi: 10.3934/cpaa.2013.12.2829

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Remarks on the approximation of the Navier-Stokes equations via the implicit Euler scheme

Michele Coti Zelati^1,

1.
Indiana University - Mathematics Department, Bloomington, IN 47405

Received: October 31, 2012

Revised: February 28, 2013

Published: October 2013

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Abstract

In this short note, we exploit the tools of multivalued dynamical systems to prove that the stationary statistical properties of the fully implicit Euler scheme converge, as the time-step parameter vanishes, to the stationary statistical properties of the two-dimensional Navier-Stokes equations.

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Mathematics Subject Classification: Primary: 37M25, 37L40; Secondary: 47H04, 47H20, 76D05.

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