A Split-Form, Stable CG/DG-SEM for Wave Propagation Modeled by Linear\n Hyperbolic Systems

2020/12/11 by David A. Kopriva, Gregor J. Gassner, Kopriva, David A. +1
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2012.06510

openalex publication_date 2020/12/11 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We present a hybrid continuous and discontinuous Galerkin spectral element\napproximation that leverages the advantages of each approach. The continuous\nGalerkin approximation is used on interior element faces where the equation\nproperties are continuous. A discontinuous Galerkin approximation is used at\nphysical boundaries and if there is a jump in properties at a face. The\napproximation uses a split form of the equations and two-point fluxes to ensure\nstability for unstructured quadrilateral/hexahedral meshes with curved\nelements. The approximation is also conservative and constant state preserving\non such meshes. Spectral accuracy is obtained for all examples, which include\nwave scattering at a discontinuous medium boundary.\n

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