Finite element Eigenvalue enclosures for the Maxwell operator

Barrenechea, G. R. and Boulton, L. and Boussaid, N. (2014) Finite element Eigenvalue enclosures for the Maxwell operator. SIAM Journal on Scientific Computing, 36 (6). A2887–A2906. ISSN 1064-8275

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    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 parameter t ∈ R. 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.