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Two Structure-Preserving Time Discretizations for Gradient Flows

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2019

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Jüngel, Ansgar
Stefanelli, Ulisse

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https://doi.org/10.1007/s00245-019-09605-x
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Applied Mathematics & Optimization. Springer. 2019, 80(3), pp. 733-764. ISSN 0095-4616. eISSN 1432-0606. Available under: doi: 10.1007/s00245-019-09605-x

Zusammenfassung

The equality between dissipation and energy drop is a structural property of gradient-flow dynamics. The classical implicit Euler scheme fails to reproduce this equality at the discrete level. We discuss two modifications of the Euler scheme satisfying an exact energy equality at the discrete level. Existence of discrete solutions and their convergence as the fineness of the partition goes to zero are discussed. Eventually, we address extensions to generalized gradient flows, GENERIC flows, and curves of maximal slope in metric spaces.

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Fachgebiet (DDC)
510 Mathematik

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Gradient flow, Structure-preserving time discretization, GENERIC flows, Curves of maximal slope

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ISO 690JÜNGEL, Ansgar, Ulisse STEFANELLI, Lara TRUSSARDI, 2019. Two Structure-Preserving Time Discretizations for Gradient Flows. In: Applied Mathematics & Optimization. Springer. 2019, 80(3), pp. 733-764. ISSN 0095-4616. eISSN 1432-0606. Available under: doi: 10.1007/s00245-019-09605-x
BibTex
@article{Jungel2019Struc-55536,
  year={2019},
  doi={10.1007/s00245-019-09605-x},
  title={Two Structure-Preserving Time Discretizations for Gradient Flows},
  number={3},
  volume={80},
  issn={0095-4616},
  journal={Applied Mathematics & Optimization},
  pages={733--764},
  author={Jüngel, Ansgar and Stefanelli, Ulisse and Trussardi, Lara}
}
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