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article

Hybridized Discontinuous Galerkin Methods for Wave Propagation

Authors:

J. PeraireAuthors Info & Claims

Journal of Scientific Computing, Volume 77, Issue 3

Pages 1566 - 1604

https://doi.org/10.1007/s10915-018-0811-x

Published: 01 December 2018 Publication History

Abstract

We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main features, display numerical results to illustrate their performance, and conclude with bibliography notes. The main ingredients in devising these DG methods are (1) a local Galerkin projection of the underlying partial differential equations at the element level onto spaces of polynomials of degree k to parametrize the numerical solution in terms of the numerical trace; (2) a judicious choice of the numerical flux to provide stability and consistency; and (3) a global jump condition that enforces the continuity of the numerical flux to obtain a global system in terms of the numerical trace. These DG methods are termed hybridized DG methods, because they are amenable to hybridization (static condensation) and hence to more efficient implementations. They share many common advantages of DG methods and possess some unique features that make them well-suited to wave propagation problems.

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cover image Journal of Scientific Computing

Journal of Scientific Computing Volume 77, Issue 3

December 2018

678 pages

ISSN:0885-7474

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Copyright © Copyright © 2018 Springer Science+Business Media, LLC, part of Springer Nature.

Publisher

Plenum Press

United States

Publication History

Published: 01 December 2018

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Nguyen NVan Heyningen RVila-Pérez JPeraire J(2024)Optimal transport for mesh adaptivity and shock capturing of compressible flowsJournal of Computational Physics10.1016/j.jcp.2024.113005508:COnline publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1016/j.jcp.2024.113005
Nguyen NPeraire J(2024)Hybridizable Discontinuous Galerkin Methods for the Two-Dimensional Monge–Ampère EquationJournal of Scientific Computing10.1007/s10915-024-02604-3100:2Online publication date: 27-Jun-2024
https://dl.acm.org/doi/10.1007/s10915-024-02604-3
Nguyen NVila-Pérez JPeraire J(2023)An adaptive viscosity regularization approach for the numerical solution of conservation lawsJournal of Computational Physics10.1016/j.jcp.2023.112507494:COnline publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1016/j.jcp.2023.112507
Guo RXing Y(2021)Optimal Energy Conserving Local Discontinuous Galerkin Methods for Elastodynamics: Semi and Fully Discrete Error AnalysisJournal of Scientific Computing10.1007/s10915-021-01418-x87:1Online publication date: 24-Feb-2021
https://dl.acm.org/doi/10.1007/s10915-021-01418-x

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