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PreprintCC BY-NC-ND 4.0arXiv

Numerical Analysis of the Virtual Element Approximation for the Smagorinsky Turbulence Model

  • Karol L. Cascavita
  • Francesca Marcon
  • Maria Strazzullo
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Abstract

In this paper, we consider the Smagorinsky model for the Navier-Stokes equations within a virtual element framework. Under the standard assumption of small data, we prove the existence and uniqueness of a solution. Assuming more regularity to the solutions, we derive the known convergence rates h for the a priori error estimates of the Smagorinsky model in two dimensional domains. We additionally prove that divergence-free virtual discretizations provide improved convergence orders, with weaker regularity assumptions than in the finite element literature. We conclude the paper with numerical results that corroborate the theory.

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Cite

BibTeXRIS
BibTeX
@misc{cascavita2026numerical,
  title = {{Numerical Analysis of the Virtual Element Approximation for the Smagorinsky Turbulence Model}},
  author = {Karol L. Cascavita and Francesca Marcon and Maria Strazzullo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02433},
  eprint = {2609.02433},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02433},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Numerical Analysis of the Virtual Element Approximation for the Smagorinsky Turbulence Model
AU  - Karol L. Cascavita
AU  - Francesca Marcon
AU  - Maria Strazzullo
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.02433
UR  - https://arxiv.org/abs/2609.02433
AB  - In this paper, we consider the Smagorinsky model for the Navier-Stokes equations within a virtual element framework. Under the standard assumption of small data, we prove the existence and uniqueness of a solution. Assuming more regularity to the solutions, we derive the known convergence rates h for the a priori error estimates of the Smagorinsky model in two dimensional domains. We additionally prove that divergence-free virtual discretizations provide improved convergence orders, with weaker regularity assumptions than in the finite element literature. We conclude the paper with numerical results that corroborate the theory.
ER  -