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Construction of trace-preserving Fortin operators

  • Franziska Eickmann
  • Tabea Tscherpel
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Abstract

We present a unifying framework to construct local Fortin operators for conforming mixed finite element pairs for the Stokes equations. The operators are constructed to satisfy the divergence-preservation property, local stability and approximation properties, and certain trace-preservation properties. For the latter, some of the finite element pairs require an enrichment of the velocity space. We present the construction for the Pd−P0 element, the Bernardi-Raugel element, the conforming Crouzeix-Raviart element, a modified MINI element and generalised Taylor-Hood elements. Furthermore, we discuss implications of the existence of such a Fortin operator beyond inf-sup stability. These include applications to non-Newtonian fluid flow, problems with inhomogeneous Dirichlet boundary conditions, as well as uniform inf-sup stability relevant for domain approximation and moving domains.

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Cite

BibTeXRIS
BibTeX
@misc{eickmann2026construction,
  title = {{Construction of trace-preserving Fortin operators}},
  author = {Franziska Eickmann and Tabea Tscherpel},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04926},
  eprint = {2609.04926},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04926},
}
RIS
TY  - UNPB
TI  - Construction of trace-preserving Fortin operators
AU  - Franziska Eickmann
AU  - Tabea Tscherpel
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.04926
UR  - https://arxiv.org/abs/2609.04926
AB  - We present a unifying framework to construct local Fortin operators for conforming mixed finite element pairs for the Stokes equations. The operators are constructed to satisfy the divergence-preservation property, local stability and approximation properties, and certain trace-preservation properties. For the latter, some of the finite element pairs require an enrichment of the velocity space. We present the construction for the P_d−P_0 element, the Bernardi-Raugel element, the conforming Crouzeix-Raviart element, a modified MINI element and generalised Taylor-Hood elements. Furthermore, we discuss implications of the existence of such a Fortin operator beyond inf-sup stability. These include applications to non-Newtonian fluid flow, problems with inhomogeneous Dirichlet boundary conditions, as well as uniform inf-sup stability relevant for domain approximation and moving domains.
ER  -