A nodal-based finite element approximation of the maxwell problem suitable for singular solutions

Santiago Badia, Ramon Codina

Research output: Contribution to journalArticleResearchpeer-review

29 Citations (Scopus)

Abstract

A new mixed finite element approximation of Maxwell's problem is proposed, its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term, which yields a very weak control on the divergence of the unknown. The method is shown to be stable and convergent in the natural H(curl 0; Ω) norm for this unknown. In particular, convergence also applies to singular solutions, for which classical nodal-based interpolations are known to suffer from spurious convergence upon mesh refinement.

Original languageEnglish
Pages (from-to)398-417
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume50
Issue number2
DOIs
Publication statusPublished - 28 May 2012
Externally publishedYes

Keywords

  • Finite elements
  • Maxwell equations
  • Nodal elements
  • Singular solutions
  • Stabilization techniques

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