On the Long-Time $H^1$-Stability of the Linearly Extrapolated BDF2 Time-Stepping Scheme for Coupled Multiphysics Flow Problems
Year: 2025
Author: Mine Akbas, Cristina Tone, Florentina Tone
Communications in Mathematical Research , Vol. 41 (2025), Iss. 2 : pp. 122–147
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2025-0013
Communications in Mathematical Research , Vol. 41 (2025), Iss. 2 : pp. 122–147
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Magnetohydrodynamics equations Boussinesq equations linearly extrapolated BDF2 timestepping scheme long-time stability.