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.
- eigenvalue enclosures
- finite element method
- spectral pollution
- Maxwell equation
Barrenechea, G. R., Boulton, L., & Boussaid, N. (2014). Finite element Eigenvalue enclosures for the Maxwell operator. SIAM Journal on Scientific Computing, 36(6), A2887–A2906. https://doi.org/10.1137/140957810