The Gradient Flow Structure of an Extended Maxwell Viscoelastic Model and a Structure-Preserving Finite Element Scheme

@article{Kimura2019TheGF,
  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={Journal of Scientific Computing},
  year={2019},
  volume={78},
  pages={1111-1131}
}
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… 
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6 Citations

Gradient Flow Model of Mode-III Fracture in Maxwell-type Viscoelastic Materials
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This paper considers semi-discrete and fully discrete mixed finite element discretizations for Maxwell-model-based problems of wave propagation in 2-dimensional linear viscoelastic solid. A large…
Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation
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Semi-discrete and fully discrete mixed finite element methods are considered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid and an unconditional stability result is derived.
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