Numerical analysis demonstrates uniform H1 dissipativity for Cauchy one-leg theta-methods in two-dimensional Navier-Stokes systems, indicating long-time numerical stability under small time steps.
In this paper we study the long‐time stability of the Cauchy one‐leg ‐methods for the two‐dimensional Navier‐Stokes equations. We establish the uniform dissipativity in , in the sense that the semi‐discrete‐in‐time approximations possess a global attractor for a small enough time step, using the discrete Grönwall lemma and the discrete uniform Grönwall lemma.
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Sanchez et al. (2026) studied this question.
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