Long-Time H1-Stability of the Cauchy One-Leg Theta-Method for the Navier-Stokes Equations
Abstract
In this paper we study the long-time stability of the Cauchy one-leg theta-methods for the two-dimensional NavierStokes equations. We establish the uniform dissipativity in H1, in the sense that the semi-discrete-in-time approximations possess a global attractor for a small enough time step, using the discrete Gronwall lemma and the discrete uniform Gronwall lemma.
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