Long‐Time H1‐Stability of the Cauchy One‐Leg θ‐Method for the Navier‐Stokes Equations
ABSTRACT 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.
Authors
- Isabel Barrio Sanchez
- Cătălin Trenchea (ORCID: https://orcid.org/0000-0002-8135-5836)
- Wenlong Pei (ORCID: https://orcid.org/0009-0009-0197-8311)
Institutions
- University of Pittsburgh (US)
- The Ohio State University (US)
Publication Details
- Journal
- Numerical Methods for Partial Differential Equations
- Published
- 2026-08-26
- DOI
- https://doi.org/10.1002/num.70137
- Primary Topic
- Stability and Controllability of Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 0.00