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PreprintCC BY 4.0arXiv

Hybrid CutFEM-IFEM model for embedded and immersed interfaces with triply-cut cells for the 2D Poisson problem

  • Darsh Nathawani
  • Christopher Kees
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Abstract

We present a hybrid CutFEM--IFEM method for 2D Poisson problems with an immersed fluid--fluid interface and an embedded fluid--solid interface on a single unfitted mesh. The proposed method leverages the strengths of both unfitted finite element methods and immersed interface techniques to handle complex interface geometries and strong discontinuities efficiently. A composite equivalent polynomial representation of the Heaviside and Dirac delta functions is used to integrate on triply-cut cells. Moreover, the IFEM basis functions are enriched with the lift functions exactly representing solution and flux jumps. Numerical examples show optimal convergence for linear and quadratic elements, with accuracy comparable to that of a mesh fitted to both interfaces.

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Cite

BibTeXRIS
BibTeX
@misc{nathawani2026hybrid,
  title = {{Hybrid CutFEM-IFEM model for embedded and immersed interfaces with triply-cut cells for the 2D Poisson problem}},
  author = {Darsh Nathawani and Christopher Kees},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38271},
  eprint = {2610.38271},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38271},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Hybrid CutFEM-IFEM model for embedded and immersed interfaces with triply-cut cells for the 2D Poisson problem
AU  - Darsh Nathawani
AU  - Christopher Kees
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38271
UR  - https://arxiv.org/abs/2610.38271
AB  - We present a hybrid CutFEM--IFEM method for 2D Poisson problems with an immersed fluid--fluid interface and an embedded fluid--solid interface on a single unfitted mesh. The proposed method leverages the strengths of both unfitted finite element methods and immersed interface techniques to handle complex interface geometries and strong discontinuities efficiently. A composite equivalent polynomial representation of the Heaviside and Dirac delta functions is used to integrate on triply-cut cells. Moreover, the IFEM basis functions are enriched with the lift functions exactly representing solution and flux jumps. Numerical examples show optimal convergence for linear and quadratic elements, with accuracy comparable to that of a mesh fitted to both interfaces.
ER  -