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A robust finite element method for incompressible magnetohydrodynamics using Whitney forms

  • Tianwei Yu
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Abstract

A stabilized semi-discrete finite element scheme for the incompressible magnetohydrodynamics system is presented. The scheme uses the Whitney $2$-form and $1$-form for the fluid velocity and magnetic induction, respectively. The key ingredient is a magnetic curl-jump penalty term, which allows us to prove a pre-asymptotic error estimate of order O(h1/2) with a constant depending on solution norms but not explicitly on the fluid viscosity and magnetic diffusivity.

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Cite

BibTeXRIS
BibTeX
@misc{yu2026robust,
  title = {{A robust finite element method for incompressible magnetohydrodynamics using Whitney forms}},
  author = {Tianwei Yu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26606},
  eprint = {2610.26606},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26606},
}
RIS
TY  - UNPB
TI  - A robust finite element method for incompressible magnetohydrodynamics using Whitney forms
AU  - Tianwei Yu
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26606
UR  - https://arxiv.org/abs/2610.26606
AB  - A stabilized semi-discrete finite element scheme for the incompressible magnetohydrodynamics system is presented. The scheme uses the Whitney $2$-form and $1$-form for the fluid velocity and magnetic induction, respectively. The key ingredient is a magnetic curl-jump penalty term, which allows us to prove a pre-asymptotic error estimate of order O(h^1/2) with a constant depending on solution norms but not explicitly on the fluid viscosity and magnetic diffusivity.
ER  -