Superconvergence and extrapolation analysis of a nonconforming mixed finite element approximation for time-harmonic Maxwell's equations

Zhonghua QIAO, Changhui Yao*, Shanghui Jia

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

In this paper, a nonconforming mixed finite element approximating to the three-dimensional time-harmonic Maxwell's equations is presented. On a uniform rectangular prism mesh, superclose property is achieved for electric field E and magnetic filed H with the boundary condition E×n=0 by means of the asymptotic expansion. Applying postprocessing operators, a superconvergence result is stated for the discretization error of the postprocessed discrete solution to the solution itself. To our best knowledge, this is the first global superconvergence analysis of nonconforming mixed finite elements for the Maxwell's equations. Furthermore, the approximation accuracy will be improved by extrapolation method.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalJournal of Scientific Computing
Volume46
Issue number1
DOIs
Publication statusPublished - Jan 2011

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Extrapolation
  • Nonconforming mixed finite element
  • Superconvergence
  • Time-harmonic Maxwell's equations

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