Approximation of singular solutions and singular data for Maxwell’s equations by Lagrange elements

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

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Abstract

A Lagrange finite element method is proposed for Maxwell’s equations in Lipschitz domains. The method is suitable for the approximation of singular solutions lying outside (H1(Ω))3⁠, with nonhomogeneous singular boundary data in the tangential trace space of H(curl;Ω) and a singular right-hand-side source term in (H0(curl;Ω))′ (the dual space of H0(curl;Ω))⁠. Numerical results are presented to illustrate performance and the theoretical results.
Original languageEnglish
Pages (from-to)771-816
Number of pages46
JournalIMA Journal of Numerical Analysis
Volume42
Issue number1
Early online date7 Jan 2021
DOIs
Publication statusPublished - Jan 2022

Keywords

  • Maxwell equations
  • Lagrange element
  • finite element method

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