Discrete compactness for the hp version of rectangular edge finite elements

Daniele Boffi, Martin Costabel, Monique Dauge, Leszek Demkowicz

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Abstract

Discretization of Maxwell eigenvalue problems with edge finite elements involves a simultaneous use of two discrete subspaces of H 1 and H(curl), reproducing the exact sequence condition. Kikuchi's discrete compactness property, along with appropriate approximability conditions, implies the convergence of discrete eigenpairs to the exact ones. In this paper we prove the discrete compactness property for the edge element approximation of Maxwell's eigenpairs on general hp adaptive rectangular meshes. Hanging nodes, yielding 1-irregular meshes, are covered, and the order of the used elements can vary from one rectangle to another, thus allowing for a real hp adaptivity. As a particular case, our analysis covers the convergence result for the p-method. © 2006 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)979-1004
Number of pages26
JournalSIAM Journal on Numerical Analysis
Volume44
Issue number3
DOIs
StatePublished - Dec 1 2006
Externally publishedYes

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