Abstract

Numerical dynamo problems involve advection–diffusion operators whose spectral and pseudospectral properties play a central role in determining growth rates, stability, and transient amplification. Their reliable numerical approximation remains challenging, particularly in advection-dominated and strongly non-normal regimes. In this talk, I present a structure-preserving finite element exterior calculus (FEEC) framework for dynamo-type advection–diffusion operators acting on differential forms. The discretization is based on finite element de Rham complexes and preserves the geometric and topological structure of the continuous problem. Within this setting, we investigate the approximation of spectra and pseudospectra and derive a priori error estimates for pseudospectral convergence. We also discuss the role of exponential transformations for advection–diffusion operators and their consequences for the asymptotic behavior of solutions.