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

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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.

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Authors and Affiliations

  1. LJAD-Laboratoire de Mathématiques “J.A. Dieudonné”, Université de Nice Sophia-Antipolis, Parc Valrose, 06108, Nice, Cedex 02, France

    Marcella Bonazzoli & Francesca Rapetti

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  1. Marcella Bonazzoli
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  2. Francesca Rapetti
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Correspondence to Francesca Rapetti.

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Bonazzoli, M., Rapetti, F. High-order finite elements in numerical electromagnetism: degrees of freedom and generators in duality. Numer Algor 74, 111–136 (2017). https://doi.org/10.1007/s11075-016-0141-8

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  • DOI: https://doi.org/10.1007/s11075-016-0141-8

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