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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

J. E. Sebold1, L. A. Lacerda2, J. A. M. Carrer3
Federal Institute of Education, Science and Technology - Campus Araquari, Santa Catarina, Brazil.
Institute of Technology for Development, Curitiba, Paraná, Brazil.
Federal University of Paraná, Curitiba, Paraná, Brazil.

Computer Modeling in Engineering & Sciences 2014, 103(2), 111-137. https://doi.org/10.3970/cmes.2014.103.111

Abstract

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.

Keywords

Numerical Methods in Engineering, Finite elements, Maxwell equations, Wave Propagation, Computational Electromagnetism.

Cite This Article

Sebold, J. E., Lacerda, L. A., A., J. (2014). 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. CMES-Computer Modeling in Engineering & Sciences, 103(2), 111–137.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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