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High-order finite elements in numerical electromagnetism: degrees of freedom and generators in duality
Authors:Marcella Bonazzoli  Francesca Rapetti
Affiliation:1.LJAD-Laboratoire de Mathématiques “J.A. Dieudonné”,Université de Nice Sophia-Antipolis,Nice,France
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:
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