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

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 h p hp -analysis is carried out and error estimates that are optimal in the meshsize h h and slightly suboptimal in the approximation degree p p are obtained.