Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

We consider a standard Adaptive Edge Finite Element Method (AEFEM) based on arbitrary order Nédélec edge elements, for three-dimensional indefinite time-harmonic Maxwell equations. We prove that the AEFEM gives a contraction for the sum of the energy error and the scaled error estimator, between two consecutive adaptive loops provided the initial mesh is fine enough. Using the geometric decay, we show that the AEFEM yields the best possible decay rate of the error plus oscillation in terms of the number of degrees of freedom. The main technical contribution of the paper is the establishment of a quasi-orthogonality and a localized a posteriori error estimator.

Original languageEnglish (US)
Pages (from-to)623-642
Number of pages20
JournalMathematics of Computation
Volume81
Issue number278
DOIs
StatePublished - Mar 30 2012

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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