TY - JOUR
T1 - On the Long-Time $H^1$-Stability of the Linearly Extrapolated BDF2 Time-Stepping Scheme for Coupled Multiphysics Flow Problems
AU - Akbas , Mine
AU - Tone , Cristina
AU - Tone , Florentina
JO - Communications in Mathematical Research 
VL - 2
SP - 122
EP - 147
PY - 2025
DA - 2025/06
SN - 41
DO - http://doi.org/10.4208/cmr.2025-0013
UR - https://global-sci.org/intro/article_detail/cmr/24188.html
KW - Magnetohydrodynamics equations, Boussinesq equations, linearly extrapolated BDF2 timestepping scheme, long-time stability.
AB - <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>