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Approximation of spectra of advection-diffusion problems: a finite element exterior calculus approach

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GSTW03 - Interactions of geometric spectral theory with numerical methods and applications

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 velocity field needed for thecompactness 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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Seminar Room, Buckingham House, New Hall Fitzwilliam College, Storey's Way, Cambridge, CB3 0DG Pavilion B Potter Room (B1.19)

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