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Research Article | Open Access

A minimizing-movements approach to GENERIC systems

Ansgar Jüngel1, Ulisse Stefanelli2,3,4( ), Lara Trussardi2
Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraß e 8-10, 1040 Wien, Austria
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria
Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währingerstraß e 17, 1090 Wien, Austria
Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, via Ferrata 1, I-27100 Pavia, Italy
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Abstract

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.

Keywords

damped harmonic oscillatorstructure-preserving time discretizationGENERIC system

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Mathematics in Engineering
Volume 4 Issue 1,
February 2022
Pages 1-18
DOI: 10.3934/mine.2022005

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Cite this article:
Jüngel A, Stefanelli U, Trussardi L. A minimizing-movements approach to GENERIC systems. Mathematics in Engineering, 2022, 4(1): 1-18. https://doi.org/10.3934/mine.2022005

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Received: 01 June 2020
Accepted: 10 May 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)