Long-Time H1-Stability of the Cauchy One-Leg Theta-Method for the Navier-Stokes Equations
arXiv:2603.2786138.91 citationsh-index: 24
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Provides theoretical stability guarantees for a class of numerical methods applied to fluid dynamics, addressing a known bottleneck in long-time simulations.
The paper proves that the Cauchy one-leg theta-methods for the 2D Navier-Stokes equations are uniformly dissipative in H^1, possessing a global attractor for sufficiently small time steps.
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 H^1, 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.