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Pre-Publicación 2019-30

Liliana Camargo, Bibiana López-Rodríguez, Mauricio Osorio, Manuel Solano:

An HDG method for Maxwell equations in heterogeneous media


We analyze a hybridizable discontinuous Galerkin (HDG) method for the time harmonic Maxwell equations arising from modeling photovoltaic solar cells. The problem is set in an inhomogeneous domain with a polyhedral connected boundary and the divergence-free condition is imposed using a Lagrange multiplier. We prove the HDG scheme is well-posed up to some frequencies and derive a stability estimate. Moreover, we prove that the method is optimal, that is, the L2-norm of the error of the approximation in both, the electric and magnetic fields, are of order h^{k+1}, where h is the meshize and k the polynomial degree of the local approximation spaces. Numerical examples are shown to validate the theory.

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Esta prepublicacion dio origen a la(s) siguiente(s) publicación(es) definitiva(s):

Liliana CAMARGO, Bibiana LóPEZ-RODRíGUEZ, Mauricio OSORIO, Manuel SOLANO: An HDG method for Maxwell equations in heterogeneous media. Computer Methods in Applied Mechanics and Engineering, vol. 368, Art. Num. 113178, (2020).