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

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.

Author Details

Mine Akbas

Cristina Tone

Florentina Tone