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. Sebold, L. A. Lacerda and J. A. M. Carrer

doi:10.3970/cmes.2014.103.111
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 103, No. 2, pp. 111-137, 2014
Download Full length paper in PDF format. Size = 696,536 bytes
Keywords Numerical Methods in Engineering, Finite elements, Maxwell equations, Wave Propagation, Computational Electromagnetism.
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.

PDF download PDF