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arXiv · 2610.01501

Finite element exterior calculus for spectra and pseudospectra of advection-diffusion of differential forms

Daniele Boffi·Kaibo Hu·Yizhou Liang·Umberto Zerbinati
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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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Daniele Boffi, Kaibo Hu, Yizhou Liang, Umberto Zerbinati. 2026-10-01. Finite element exterior calculus for spectra and pseudospectra of advection-diffusion of differential forms. https://arxiv.org/abs/2610.01501

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