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A quasi-interpolation method for finite element spaces

  • Ohannes Karakashian
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Abstract

A combination of Taylor polynomial approximation and averaging results in a powerful quasi-interpolation technique that can be used to analyze the approximation properties of finite element spaces. With this particular approach, the notion of affine equivalent families is completely bypassed in the sense that the degrees of freedom are defined locally rather than being exported from a reference element. In particular, domains with curved boundaries can be handled in a natural manner. Finally, the ease of its application to a particular finite element makes it a valuable pedagogical tool.

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Cite

BibTeXRIS
BibTeX
@misc{karakashian2026quasiinterpolation,
  title = {{A quasi-interpolation method for finite element spaces}},
  author = {Ohannes Karakashian},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10374},
  eprint = {2609.10374},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10374},
}
RIS
TY  - UNPB
TI  - A quasi-interpolation method for finite element spaces
AU  - Ohannes Karakashian
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10374
UR  - https://arxiv.org/abs/2609.10374
AB  - A combination of Taylor polynomial approximation and averaging results in a powerful quasi-interpolation technique that can be used to analyze the approximation properties of finite element spaces. With this particular approach, the notion of affine equivalent families is completely bypassed in the sense that the degrees of freedom are defined locally rather than being exported from a reference element. In particular, domains with curved boundaries can be handled in a natural manner. Finally, the ease of its application to a particular finite element makes it a valuable pedagogical tool.
ER  -