A finite element method for a curlcurl-graddiv eigenvalue interface problem

Huoyuan Duan, Ping Lin (Lead / Corresponding author), Roger C. E. Tan

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4 Citations (Scopus)
154 Downloads (Pure)

Abstract

In this paper we propose and study a finite element method for a curlcurl-graddiv eigenvalue interface problem. Its solution may be of piecewise non-H1. We would like to approximate such a solution in an H1-conforming finite element space. With the discretizations of both curl and div operators of the underlying eigenvalue problem in two finite element spaces, the proposed
method is essentially a standard H1-conforming element method, up to element bubbles which can be statically eliminated at element levels. We first analyze the proposed method for the related source interface problem by establishing the stability and the error bounds. We then analyze the underlying eigenvalue interface problem, and we obtain the error bounds O(h2r0 ) for eigenvalues
which correspond to eigenfunctions in QJ
j=1(Hr
(Ωj ))3
,→ (Hr0 (Ω))3
space, where the piecewise
regularity r and the global regularity r0 may belong to the most interesting interval [0, 1].
Original languageEnglish
Pages (from-to)1193-1228
Number of pages36
JournalSIAM Journal on Numerical Analysis
Volume54
Issue number2
Early online date14 Apr 2016
DOIs
Publication statusPublished - 2016

Keywords

  • generalized Maxwell eigenvalue problem of curlcurl-graddiv operator
  • H 1 -conforming finite element method
  • piecewise non H 1 -space solution
  • error estimates
  • spectral correctness

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