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Computational SeismologyA Practical Introduction$
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Heiner Igel

Print publication date: 2016

Print ISBN-13: 9780198717409

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780198717409.001.0001

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The Discontinuous Galerkin Method

The Discontinuous Galerkin Method

(p.239) 9 The Discontinuous Galerkin Method
Computational Seismology

Heiner Igel

Oxford University Press

The discontinuous Galerkin method is introduced as a special type of finite-element method in which the solution fields are allowed to be discontinuous at the element boundaries. This requires the use of the same fluxes as introduced in the chapter on the finite-volume method. The solution field is interpolated using Lagrange polynomials. The discontinuous Galerkin principle leads to an elemental system of equations. Communication between elements is possible through the fluxes. The method is presented for scalar and elastic wave equations for both homogeneous and heterogeneous media. The method can be considered a mixture of the spectral-element and the finite-volume methods.

Keywords:   discontinuous Galerkin method, Riemann problem, Lagrange polynomials, fluxes, scalar advection, hyperbolic systems

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