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

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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.

Author Biographies

  • Mine Akbas
    Engineering Fundamental Sciences, Tarsus University, Tarsus 33400, Türkiye
  • Cristina Tone
    Department of Mathematics, University of Louisville, Louisville, KY 40292, USA
  • Florentina Tone
    Department Mathematics and Statistics, University of West Florida, Pensacola, FL 32514, USA
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DOI

10.4208/cmr.2025-0013

How to Cite

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