Finite element eigenvalue enclosures for the Maxwell operator

2014/02/20 by Barrenechea, Gabriel Raúl, Boulton, Lyonell, Boussaid, Nabile
#Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1402.4911

Abstract

We propose employing the extension of the Lehmann-Maehly-Goerisch method developed by Zimmermann and Mertins, as a highly effective tool for the pollution-free finite element computation of the eigenfrequencies of the resonant cavity problem on a bounded region. This method gives complementary bounds for the eigenfrequencies which are adjacent to a given real parameter. We present a concrete numerical scheme which provides certified enclosures in a suitable asymptotic regime. We illustrate the applicability of this scheme by means of some numerical experiments on benchmark data using Lagrange elements and unstructured meshes.

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