The gradient flow structure of an extended Maxwell viscoelastic model and a structure-preserving finite element scheme
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2018
- arXiv:
- arXiv:1802.05566
- Bibcode:
- 2018arXiv180205566K
- Keywords:
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- Mathematics - Numerical Analysis
- E-Print:
- Journal of Scientific Computing, 78(2019), 1111-1131