Optimal error estimates for Nedelec edge elements for time-harmonic Maxwell's equations

Liuqiang Zhong*, Shi Shu, Gabriel Wittum, Jinchao Xu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

In this paper, we obtain optimal error estimates in both L2-norm and H(curl)-norm for the Nedelec edge finite element approximation of the time-harmonic Maxwell's equations on a general Lipschitz domain discretized on quasi-uniform meshes. One key to our proof is to transform the L2 error estimates into the L2 estimate of a discrete divergence-free function which belongs to the edge finite element spaces, and then use the approximation of the discrete divergence-free function by the continuous divergence-free function and a duality argument for the continuous divergence-free function. For Nédélec's second type elements, we present an optimal convergence estimate which improves the best results available in the literature.

Original languageEnglish (US)
Pages (from-to)563-572
Number of pages10
JournalJournal of Computational Mathematics
Volume27
Issue number5
DOIs
StatePublished - Sep 2009
Externally publishedYes

Keywords

  • Edge finite element
  • Time-harmonic Maxwell's equations

ASJC Scopus subject areas

  • Computational Mathematics

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