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

Liuqiang Zhong, Shi Shu, Gabriel Wittum, Jinchao Xu

Research output: Contribution to journalArticlepeer-review

34 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. Copyright 2009 by AMSS, Chinese Academy of Sciences.
Original languageEnglish (US)
Pages (from-to)563-572
Number of pages10
JournalJournal of Computational Mathematics
Volume27
Issue number5
DOIs
StatePublished - Sep 1 2009
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

  • Computational Mathematics

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