High-order accurate discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations

Abstract

We introduce a high-order accurate discontinuous Galerkin (DG) method for the indefinite frequency-domain Maxwell equations in three spatial dimensions. The novelty of the method lies in the way the numerical flux is computed. Instead of using the more popular local discontinuous Galerkin (LDG) or interior-penalty discontinuous Galerkin (IP-DG) numerical fluxes, we opt for a formulation which makes use of the local lifting operator. This allows us to choose a penalty parameter that is independent of the mesh size and the polynomial order. Moreover, we use a hierarchic construction of $H$(curl)-conforming basis functions, the first-order version of which correspond to the second family of Nédélec elements. We also provide a priori error bounds for our formulation, and carry out three-dimensional numerical experiments to validate the theoretical results