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.