PreprintCC BY 4.0arXiv
Finite element exterior calculus for spectra and pseudospectra of advection-diffusion of differential forms
Abstract
Numerical investigations of dynamo action have remained active in fluid mechanics over the past decades, presenting numerous challenges and open problems. Meanwhile, the development of structure-preserving methods and finite element exterior calculus (FEEC) inspires a revisit of numerical dynamo studies and an exploration of existing open questions in computation. In this paper, we present a FEEC approach for dynamo problems. In particular, we investigate structure-preserving finite element schemes for computing the spectra and pseudospectra of advection-diffusion operators of differential forms. The schemes and their analysis are based on finite element de Rham complexes.
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BibTeX
@misc{boffi2026finite,
title = {{Finite element exterior calculus for spectra and pseudospectra of advection-diffusion of differential forms}},
author = {Daniele Boffi and Kaibo Hu and Yizhou Liang and Umberto Zerbinati},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01501},
eprint = {2610.01501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01501},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite element exterior calculus for spectra and pseudospectra of advection-diffusion of differential forms
AU - Daniele Boffi
AU - Kaibo Hu
AU - Yizhou Liang
AU - Umberto Zerbinati
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01501
UR - https://arxiv.org/abs/2610.01501
AB - Numerical investigations of dynamo action have remained active in fluid mechanics over the past decades, presenting numerous challenges and open problems. Meanwhile, the development of structure-preserving methods and finite element exterior calculus (FEEC) inspires a revisit of numerical dynamo studies and an exploration of existing open questions in computation. In this paper, we present a FEEC approach for dynamo problems. In particular, we investigate structure-preserving finite element schemes for computing the spectra and pseudospectra of advection-diffusion operators of differential forms. The schemes and their analysis are based on finite element de Rham complexes.
ER -