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Volume 41, Issue 2
On the Long-Time $H^1$-Stability of the Linearly Extrapolated BDF2 Time-Stepping Scheme for Coupled Multiphysics Flow Problems

Mine Akbas, Cristina Tone & Florentina Tone

DOI: 10.4208/cmr.2025-0013

Commun. Math. Res., 41 (2025), pp. 122-147.

Published online: 2025-06

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  • 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.

  • Keywords

Magnetohydrodynamics equations, Boussinesq equations, linearly extrapolated BDF2 timestepping scheme, long-time stability.

  • AMS Subject Headings

35Q56, 35Q35

  • Copyright

COPYRIGHT: © Global Science Press

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@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 = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2025-0013}, url = {http://global-sci.org/intro/article_detail/cmr/24188.html} }
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 -

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.

Akbas , MineTone , Cristina and Tone , Florentina. (2025). On the Long-Time $H^1$-Stability of the Linearly Extrapolated BDF2 Time-Stepping Scheme for Coupled Multiphysics Flow Problems. Communications in Mathematical Research . 41 (2). 122-147. doi:10.4208/cmr.2025-0013
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