The local discontinuous Galerkin method for the numerical approximation of the time-harmonic Maxwell equations in low-frequency regime is introduced and analyzed. We consider topologically non-trivial domains and heterogeneous media, containing both conducting and insulating materials. The presented method involves discontinuous Galerkin discretizations of the curl-curl and grad-div operators, based on a mixed formulation of the problem and on the introduction of the so-called numerical fluxes. An hp-analysis is carried out and error estimates that are optimal in the meshsize h and slightly suboptimal in the approximation degree p are obtained.
Institute for Mathematics and Its Applications>IMA Preprints Series
Perugia, Ilaria; Schotzau, Dominik.
The hp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell's equations.
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