Analysis of an Hp-Non-conforming Discontinuous Galerkin Spectral Element Method for Wave
TEXAS UNIV AT AUSTIN INST FOR COMPUTATIONAL ENGINEERING AND SCIENCES
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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.
- Numerical Mathematics