Convergence of Lagrange finite elements for the Maxwell eigenvalue problem in two dimensions

Daniele Boffi, Johnny Guzman, Michael Neilan

Research output: Contribution to journalArticlepeer-review

Abstract

We consider finite element approximations of the Maxwell eigenvalue problem in two dimensions. We prove, in certain settings, convergence of the discrete eigenvalues using Lagrange finite elements. In particular, we prove convergence in three scenarios: piecewise linear elements on Powell–Sabin triangulations, piecewise quadratic elements on Clough–Tocher triangulations and piecewise quartics (and higher) elements on general shape-regular triangulations. We provide numerical experiments that support the theoretical results. The computations also show that, on general triangulations, the eigenvalue approximations are very sensitive to nearly singular vertices, i.e., vertices that fall on exactly two ‘almost’ straight lines.
Original languageEnglish (US)
JournalIMA Journal of Numerical Analysis
DOIs
StatePublished - Feb 23 2022

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • General Mathematics

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