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Numerical Algorithms

, Volume 74, Issue 1, pp 111–136 | Cite as

High-order finite elements in numerical electromagnetism: degrees of freedom and generators in duality

  • Marcella Bonazzoli
  • Francesca Rapetti
Original Paper

Abstract

Explicit generators for high-order (r>1) scalar and vector finite element spaces generally used in numerical electromagnetism are presented and classical degrees of freedom, the so-called moments, revisited. Properties of these generators on simplicial meshes are investigated, and a general technique to restore duality between moments and generators is proposed. Algebraic and exponential optimal h- and r-error rates are numerically validated for high-order edge elements on the problem of Maxwell’s eigenvalues in a square domain.

Keywords

High-order FEs in electromagnetism Degrees of freedom and generators in duality Simplices 

Mathematics Subject Classification (2010)

78M10 65N30 68U20 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.LJAD-Laboratoire de Mathématiques “J.A. Dieudonné”Université de Nice Sophia-AntipolisNiceFrance

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