Maximum time step for the BDF3 scheme applied to gradient flows

Calcolo volume 58, Article number: 3 (2021) Cite this article

Abstract

For backward differentiation formulae (BDF) applied to gradient flows of semiconvex functions, quadratic stability implies the existence of a Lyapunov functional. We compute the maximum time step which can be derived from quadratic stability for the 3-step BDF method (BDF3). Applications to the asymptotic behaviour of sequences generated by the BDF3 scheme are given.

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Acknowledgements

The author is thankful to Frédéric Bosio, Anass Bouchriti and Nour Eddine Alaa for helpful discussions. The author also wishes to thank the anonymous referee for his valuable comments.

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  1. Laboratoire de Mathématiques et Applications, Université de Poitiers, CNRS, F-86073, Poitiers, France

    Morgan Pierre

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  1. Morgan Pierre
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Correspondence to Morgan Pierre.

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Pierre, M. Maximum time step for the BDF3 scheme applied to gradient flows. Calcolo 58, 3 (2021). https://doi.org/10.1007/s10092-020-00393-3

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Keywords

  • Gradient system
  • BDF method
  • Semiconvex function
  • Kurdyka–Łojasiewicz property
  • Multivalued dynamical system

Mathematics Subject Classification

  • 65P40
  • 65L04