High-Order Divergence-Conforming Constrained Bases for Triangular Cells

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4 Scopus citations


This paper presents an algebraic technique for generating arbitrary-order divergence-conforming bases for curvilinear triangular cells. The bases are constructed by enforcing appropriate constraints on a linear combination of general functions and then extracting the desired bases using singular value decompositions. Koornwinder-Dubiner polynomials are chosen as the general function set. Basic constraints are presented to obtain divergence-conforming bases, and additional constraints are presented to further enforce the bases to be Nédélec. Results from a variety of problems are given to show that the bases exhibit high-order convergence and also produce systems that are relatively well conditioned compared to other basis sets.

Original languageEnglish
Article number7967697
Pages (from-to)4717-4727
Number of pages11
JournalIEEE Transactions on Antennas and Propagation
Issue number9
StatePublished - Sep 2017

Bibliographical note

Publisher Copyright:
© 2017 IEEE.


  • Constrained bases
  • Koornwinder-Dubiner polynomials
  • singular value decomposition (SVD)
  • triangle cells

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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