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WHITNEY/NE´DE´ LEC ELEMENTS METHOD APPROACH APPLIED IN THE MAXWELL’S EQUATIONS

WHITNEY/NÉDÉ LEC ELEMENTS METHOD APPROACH APPLIED IN THE MAXWELL’S EQUATIONS

Sebold, Jean Eduardo; Oliveira, Saulo Pomponet; Lacerda, Luiz Alkimin de; Carrer, José Antonio Marques;

Artigo Completo:

This work concerns Whitney and N´ed´elec finite element methods for time-harmonic Maxwell’s equations. We review the derivation of the harmonic equations from full Maxwell’s equations as well as their variational formulation, and build the Whitney and N´ed´elec element spaces, whose functions have continuous tangential components along the interface of adjacent elements. We study the dispersive behaviour of first-order N´ed´elec elements in two and three dimensions, in terms of the time frequency and the mesh element size, and present an explicit form for the discrete dispersion relation. Numerical experiments validate the performance of Whitney elements and N´ed´elec first order in a two-dimensional domain, that also illustrates the dispersion of the approximate solution with respect to the exact solution. The discrete dispersion relation for elements of the first order, show, through numerical evidence that the numerical phase velocity can be used as an error estimator in the Whitney and N´ed´elec finite element approximation, and thus, display an initial parameter h to the mesh refinement.

Artigo Completo:

This work concerns Whitney and N´ed´elec finite element methods for time-harmonic Maxwell’s equations. We review the derivation of the harmonic equations from full Maxwell’s equations as well as their variational formulation, and build the Whitney and N´ed´elec element spaces, whose functions have continuous tangential components along the interface of adjacent elements. We study the dispersive behaviour of first-order N´ed´elec elements in two and three dimensions, in terms of the time frequency and the mesh element size, and present an explicit form for the discrete dispersion relation. Numerical experiments validate the performance of Whitney elements and N´ed´elec first order in a two-dimensional domain, that also illustrates the dispersion of the approximate solution with respect to the exact solution. The discrete dispersion relation for elements of the first order, show, through numerical evidence that the numerical phase velocity can be used as an error estimator in the Whitney and N´ed´elec finite element approximation, and thus, display an initial parameter h to the mesh refinement.

Palavras-chave: Whitney Elements, N´ed´elec Elements, Legendre hierarchical basis functions, Whitney Elements, N´ed´elec Elements, Legendre hierarchical basis functions,

Palavras-chave: ,

DOI: 10.5151/mathpro-cnmai-0011

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Como citar:

Sebold, Jean Eduardo; Oliveira, Saulo Pomponet; Lacerda, Luiz Alkimin de; Carrer, José Antonio Marques; "WHITNEY/NE´DE´ LEC ELEMENTS METHOD APPROACH APPLIED IN THE MAXWELL’S EQUATIONS", p. 20-29 . In: Anais do Congresso Nacional de Matemática Aplicada à Indústria [= Blucher Mathematical Proceedings, v.1, n.1]. São Paulo: Blucher, 2015.
ISSN em b-reve, DOI 10.5151/mathpro-cnmai-0011

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