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PreprintCC BY 4.0arXiv

A virtual element method for Kelvin--Voigt viscoelasticity

  • Utkarsh Rajput
  • Ankit Kumar
  • Andres E. Rubiano
  • Ricardo Ruiz-Baier
  • Sarvesh Kumar
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Abstract

Considering the computational advantages of virtual element methods (VEM), this work employs a conforming VEM for the numerical approximation of the Kelvin--Voigt model of viscoelasticity. For clarity and simplicity, we focus on the primal formulation. The spatial discretization is carried out using the virtual element method, while the temporal discretization is handled via the {second-order Crank--Nicolson} scheme. We establish the well-posedness of both the semi-discrete and fully discrete problems and derive {\it a priori} error estimates. Several representative numerical examples are presented to validate the theoretical results and to demonstrate the effectiveness of the proposed formulation.

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Cite

BibTeXRIS
BibTeX
@misc{rajput2026virtual,
  title = {{A virtual element method for Kelvin--Voigt viscoelasticity}},
  author = {Utkarsh Rajput and Ankit Kumar and Andres E. Rubiano and Ricardo Ruiz-Baier and Sarvesh Kumar},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10908},
  eprint = {2609.10908},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10908},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A virtual element method for Kelvin--Voigt viscoelasticity
AU  - Utkarsh Rajput
AU  - Ankit Kumar
AU  - Andres E. Rubiano
AU  - Ricardo Ruiz-Baier
AU  - Sarvesh Kumar
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10908
UR  - https://arxiv.org/abs/2609.10908
AB  - Considering the computational advantages of virtual element methods (VEM), this work employs a conforming VEM for the numerical approximation of the Kelvin--Voigt model of viscoelasticity. For clarity and simplicity, we focus on the primal formulation. The spatial discretization is carried out using the virtual element method, while the temporal discretization is handled via the {second-order Crank--Nicolson} scheme. We establish the well-posedness of both the semi-discrete and fully discrete problems and derive {\it a priori} error estimates. Several representative numerical examples are presented to validate the theoretical results and to demonstrate the effectiveness of the proposed formulation.
ER  -