@Article{CMR-41-122,
author = {Akbas , MineTone , Cristina and Tone , Florentina},
title = {On the Long-Time $H^1$-Stability of the Linearly Extrapolated BDF2 Time-Stepping Scheme for Coupled Multiphysics Flow Problems},
journal = {Communications in Mathematical Research },
year = {2025},
volume = {41},
number = {2},
pages = {122--147},
abstract = {<p style="text-align: justify;">The purpose of the current article is to study the $H^1$-stability for all
positive time of the linearly extrapolated BDF2 time-stepping scheme for the
magnetohydrodynamics and Boussinesq equations. Specifically, we discretize
in time using the linearly backward differentiation formula, and by employing
both the discrete Gronwall lemma and the discrete uniform Gronwall lemma,
we establish that each numerical scheme is uniformly bounded in the $H^1$-norm.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2025-0013},
url = {http://global-sci.org/intro/article_detail/cmr/24188.html}
}