Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 23 min ago
PreprintarXiv licencearXiv

Discrete Sobolev and Trudinger inequalities on polyhedral meshes

  • Maxime Herda
  • Ariane Trescases
  • Antoine Zurek
Open at sourcePDFDOICite

Abstract

We revisit the derivation of discrete Sobolev and related inequalities on bounded domains for piecewise constant functions on polyhedral meshes. Our results improve the dependence of the Sobolev constant on the Lebesgue exponents and allow us to recover the asymptotics of the continuous case. As a consequence we derive a discrete version of the Trudinger inequality and variants. We extend our results to broken Sobolev spaces and discuss implications of these new or refined discrete functional inequalities in the numerical analysis of non-conforming numerical methods.

Related

  1. Uniform discrete Poincaré inequalities for Hybrid High-Order differential forms on polyhedral meshes
    Silvano Pitassi
    HALPreprintCC BY 4.0Full textNumerical analysis & scientific computingHALarXiv
  2. Improved Sobolev and Moser--Trudinger--Onofri Inequalities under Constraints: Sharpness and Quantitative Remainders
    Yuxuan Zhou, Wenming Zou
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  3. Sobolev--Poincaré inequalities for piecewise W2,p functions over general polytopic meshes
    Michele Botti, Lorenzo Mascotto
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv
  4. The Zipped Finite Element Method on polyhedral meshes
    Stefano Berrone, Gioana Teora
    arXivPreprintCC BY-NC-ND 4.0Full textNumerical analysis & scientific computingarXiv
  5. Trudinger-Moser type inequality in fractional Sobolev space with singularity on smooth submanifold
    Vivek Sahu
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{herda2026discrete,
  title = {{Discrete Sobolev and Trudinger inequalities on polyhedral meshes}},
  author = {Maxime Herda and Ariane Trescases and Antoine Zurek},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28152},
  eprint = {2609.28152},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28152},
}
RIS
TY  - UNPB
TI  - Discrete Sobolev and Trudinger inequalities on polyhedral meshes
AU  - Maxime Herda
AU  - Ariane Trescases
AU  - Antoine Zurek
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28152
UR  - https://arxiv.org/abs/2609.28152
AB  - We revisit the derivation of discrete Sobolev and related inequalities on bounded domains for piecewise constant functions on polyhedral meshes. Our results improve the dependence of the Sobolev constant on the Lebesgue exponents and allow us to recover the asymptotics of the continuous case. As a consequence we derive a discrete version of the Trudinger inequality and variants. We extend our results to broken Sobolev spaces and discuss implications of these new or refined discrete functional inequalities in the numerical analysis of non-conforming numerical methods.
ER  -