Extrapolation of mixed finite element approximations for the Maxwell eigenvalue problem

Changhui Yao, Zhonghua Qiao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)

Abstract

In this paper, a general method to derive asymptotic error expansion formulas for the mixed finite element approximations of the Maxwell eigenvalue problem is established. Abstract lemmas for the error of the eigenvalue approximations are obtained. Based on the asymptotic error expansion formulas, the Richardson extrapolation method is employed to improve the accuracy of the approximations for the eigenvalues of the Maxwell system from O(h2) to O(h4) when applying the lowest order Nédélec mixed finite element and a nonconforming mixed finite element. To our best knowledge, this is the first superconvergence result of the Maxwell eigenvalue problem by the extrapolation of the mixed finite element approximation. Numerical experiments are provided to demonstrate the theoretical results.
Original languageEnglish
Pages (from-to)379-395
Number of pages17
JournalNumerical Mathematics
Volume4
Issue number3
DOIs
Publication statusPublished - 1 Aug 2011
Externally publishedYes

Keywords

  • Asymptotic error expansion
  • Maxwell eigenvalue problem
  • Mixed finite element
  • Richardson extrapolation

ASJC Scopus subject areas

  • Modelling and Simulation
  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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