The gradient flow structure of an extended Maxwell viscoelastic model and a structure-preserving finite element scheme
Numerical Analysis
2021-07-22 v2
Abstract
An extended Maxwell viscoelastic model with a relaxation parameter is studied from mathematical and numerical points of view. It is shown that the model has a gradient flow property with respect to a viscoelastic energy. Based on the gradient flow structure, a structure-preserving time-discrete model is proposed and existence of a unique solution is proved. Moreover, a structure-preserving P1/P0 finite element scheme is presented and its stability in the sense of energy is shown by using its discrete gradient flow structure. As typical viscoelastic phenomena, two-dimensional numerical examples by the proposed scheme for a creep deformation and a stress relaxation are shown and the effects of the relaxation parameter are investigated.
Keywords
Cite
@article{arxiv.1802.05566,
title = {The gradient flow structure of an extended Maxwell viscoelastic model and a structure-preserving finite element scheme},
author = {Masato Kimura and Hirofumi Notsu and Yoshimi Tanaka and Hiroki Yamamoto},
journal= {arXiv preprint arXiv:1802.05566},
year = {2021}
}