TY - JOUR
T1 - A minimizing-movements approach to GENERIC systems
AU - Jüngel, Ansgar
AU - Stefanelli, Ulisse
AU - Trussardi, Lara
N1 - Publisher Copyright:
© 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)
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Damped harmonic oscillator
KW - GENERIC system
KW - Structure-preserving time discretization
UR - http://www.scopus.com/inward/record.url?scp=85108602711&partnerID=8YFLogxK
U2 - 10.3934/MINE.2022005
DO - 10.3934/MINE.2022005
M3 - Article
SN - 2640-3501
VL - 4
JO - Mathematics in Engineering
JF - Mathematics in Engineering
IS - 1
ER -