We consider structure-preserving finite element schemes for the approximation of spectra of advection-diffusion operators for differential forms. This is a non trivial generalization of the classical analysis of the Maxwell cavity eigenproblem. A crucial aspect is related to the regularity of the flux velocity field needed for the compactness of the underlying problem.
Applications include the dynamo theory in magneto hydrodynamics.
We present numerical results involving the computation of spectra and pseudo-spectra of non-normal operators.
This is a joint work with Kaibo Hu, Yizhou Liang, and Umberto Zerbinati.