Construction of an Edge Finite Element Space and a Contribution to the Mesh Selection in the Approximation of the Second Order Time Harmonic Maxwell System

This work is concerned with the development of the so-called Whitney and Nédélec edge finite element method for the solution of the time-harmonic Maxwell equations. Initially, the second order time harmonic Maxwell systems, as well as their variational formulation, are presented. In the sequence, Wh...

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Bibliographic Details
Published in:Computer modeling in engineering & sciences Vol. 103; no. 2; pp. 111 - 137
Main Authors: Sebold, J E, Lacerda, L A, Carrer, J A M
Format: Journal Article
Language:English
Published: Henderson Tech Science Press 2014
Subjects:
Approximation
Continuity (mathematics)
Dispersions
Estimators
Finite element method
Grid refinement (mathematics)
Harmonics
Mathematical analysis
Mathematical models
Maxwell equation
Maxwell's equations
Nonlinear programming
Phase velocity
ISSN:1526-1492, 1526-1506
Online Access:Get full text
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Summary:This work is concerned with the development of the so-called Whitney and Nédélec edge finite element method for the solution of the time-harmonic Maxwell equations. Initially, the second order time harmonic Maxwell systems, as well as their variational formulation, are presented. In the sequence, Whitney and Nédélec element spaces, whose functions present continuous tangential components along the interface are built of adjacent elements. Then, numerical experiments validate the performance of Whitney and Nédélec first order elements in a two-dimensional domain. The discrete dispersion relation for the elements shows that the numerical phase velocity can be used as an error estimator. Consequently, it becomes possible to define an initial parameter to the mesh refinement that, by its turn, can make the phase difference negligible.
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ISSN:1526-1492
1526-1506
DOI:10.3970/cmes.2014.103.111