Analysis of an Hp-Non-conforming Discontinuous Galerkin Spectral Element Method for Wave

We analyze the consistency, stability, and convergence of an hp discontinuous Galerkin spectral element method. The analysis is carried out simultaneously for acoustic, elastic, coupled elastic–acoustic, and electromagnetic wave propagation. Our analytical results are developed for both conforming and non-conforming approximations on hexahedral meshes using either exact integration with Legendre-Gauss quadrature or inexact integration with Legendre-Gauss-Lobatto quadrature. A mortar-based non-conforming approximation is developed to treat both h and p non-conforming meshes simultaneously. The mortar approach is constructed in such a way that consistency, stability, and convergence analyses for non-conforming approximations follows the conforming counterparts with minimal modifications. In particular, sharp hp-convergence results are proved for non-conforming approximations for time dependent wave propagation problems using inexact quadrature.