WHITNEY/NE´DE´ LEC ELEMENTS METHOD APPROACH APPLIED IN THE MAXWELL’S EQUATIONS
| Autor: | Saulo Pomponet Oliveira, Jean Eduardo Sebold, J.A.M. Carrer, Luiz Alkimin de Lacerda |
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| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
Computer science Mathematical analysis Estimator Harmonic (mathematics) Finite element method Domain (mathematical analysis) Mathematics::Numerical Analysis symbols.namesake Exact solutions in general relativity Maxwell's equations Dispersion relation symbols Dispersion (water waves) |
| Zdroj: | Anais do Congresso Nacional de Matemática Aplicada à Indústria. |
| DOI: | 10.5151/mathpro-cnmai-0011 |
| Popis: | This work concerns Whitney and Nedelec 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 Nedelec element spaces, whose functions have continuous tangential components along the interface of adjacent elements. We study the dispersive behaviour of first-order Nedelec 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 Nedelec 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 Nedelec finite element approximation, and thus, display an initial parameter h to the mesh refinement. |
| Databáze: | OpenAIRE |
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