A minimizing-movements approach to GENERIC systems

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2022
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Jüngel, Ansgar
Stefanelli, Ulisse
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Mathematics in Engineering. AIMS Press. 2022, 4(1), pp. 1-18. eISSN 2640-3501. Available under: doi: 10.3934/mine.2022005
Zusammenfassung

We present a new time discretization scheme adapted to the structure of GENERIC systems. The scheme is based on incremental minimization and is therefore variational in nature. The GENERIC structure of the scheme provides stability and conditional convergence. We show that the scheme can be rigorously implemented in the classical case of the damped harmonic oscillator. Numerical evidence is collected, illustrating the performance of the method and, in particular, the conservation of the energy at the discrete level.

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Fachgebiet (DDC)
510 Mathematik
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damped harmonic oscillator, structure-preserving time discretization, GENERIC system
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ISO 690JÜNGEL, Ansgar, Ulisse STEFANELLI, Lara TRUSSARDI, 2022. A minimizing-movements approach to GENERIC systems. In: Mathematics in Engineering. AIMS Press. 2022, 4(1), pp. 1-18. eISSN 2640-3501. Available under: doi: 10.3934/mine.2022005
BibTex
@article{Jungel2022minim-55529,
  year={2022},
  doi={10.3934/mine.2022005},
  title={A minimizing-movements approach to GENERIC systems},
  number={1},
  volume={4},
  journal={Mathematics in Engineering},
  pages={1--18},
  author={Jüngel, Ansgar and Stefanelli, Ulisse and Trussardi, Lara}
}
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