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PreprintCC BY 4.0arXiv

Anisotropic error estimates for the L2-projection onto discontinuous finite element spaces

  • Joaquín Valenzuela Díaz
  • Yuan Wang
  • Sander Rhebergen
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Abstract

Anisotropic error estimates are determined for the L2-orthogonal projection onto discontinuous finite element spaces in two and three dimensions. These estimates are determined in Wm,p-seminorms, in which p ∈ [1,∞] and 0 ≤ m ≤ k+1, where k ≥ 0 is the polynomial degree. The analysis relies on a geometric condition that is equivalent to the maximum angle condition. As an application, an apriori error analysis is presented for a hybridizable discontinuous Galerkin discretization of the Poisson problem on two and three dimensional anisotropic meshes.

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Cite

BibTeXRIS
BibTeX
@misc{diaz2026anisotropic,
  title = {{Anisotropic error estimates for the $L^2$-projection onto discontinuous finite element spaces}},
  author = {Joaquín Valenzuela Díaz and Yuan Wang and Sander Rhebergen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38892},
  eprint = {2610.38892},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38892},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Anisotropic error estimates for the L^2-projection onto discontinuous finite element spaces
AU  - Joaquín Valenzuela Díaz
AU  - Yuan Wang
AU  - Sander Rhebergen
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38892
UR  - https://arxiv.org/abs/2610.38892
AB  - Anisotropic error estimates are determined for the L^2-orthogonal projection onto discontinuous finite element spaces in two and three dimensions. These estimates are determined in W^m,p-seminorms, in which p ∈ [1,∞] and 0 ≤ m ≤ k+1, where k ≥ 0 is the polynomial degree. The analysis relies on a geometric condition that is equivalent to the maximum angle condition. As an application, an apriori error analysis is presented for a hybridizable discontinuous Galerkin discretization of the Poisson problem on two and three dimensional anisotropic meshes.
ER  -