The ℎ𝑝-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations

Perugia, Ilaria; Schötzau, Dominik

doi:10.1090/S0025-5718-02-01471-0

The $hp$-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations
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by Ilaria Perugia and Dominik Schötzau PDF

Math. Comp. 72 (2003), 1179-1214 Request permission

Abstract:

The local discontinuous Galerkin method for the numerical approximation of the time-harmonic Maxwell equations in a low-frequency regime is introduced and analyzed. Topologically nontrivial domains and heterogeneous media are considered, containing both conducting and insulating materials. The presented method involves discontinuous Galerkin discretizations of the curl-curl and grad-div operators, derived by introducing suitable auxiliary variables and 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.

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