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Optimal Discontinuous Galerkin Methods for Wave Propagation

Chung, Eric T. and Engquist, Björn (2006) Optimal Discontinuous Galerkin Methods for Wave Propagation. SIAM Journal on Numerical Analysis, 44 (5). pp. 2131-2158. ISSN 0036-1429. http://resolver.caltech.edu/CaltechAUTHORS:CHUsiamjco06

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Abstract

We have developed and analyzed a new class of discontinuous Galerkin methods (DG) which can be seen as a compromise between standard DG and the finite element (FE) method in the way that it is explicit like standard DG and energy conserving like FE. In the literature there are many methods that achieve some of the goals of explicit time marching, unstructured grid, energy conservation, and optimal higher order accuracy, but as far as we know only our new algorithms satisfy all the conditions. We propose a new stability requirement for our DG. The stability analysis is based on the careful selection of the two FE spaces which verify the new stability condition. The convergence rate is optimal with respect to the order of the polynomials in the FE spaces. Moreover, the convergence is described by a series of numerical experiments.


Item Type:Article
Additional Information:©2006 Society for Industrial and Applied Mathematics Received by the editors September 26, 2005; accepted for publication (in revised form) April 6, 2006; published electronically November 3, 2006
Subject Keywords:discontinuous Galerkin; wave propagation; optimal rate of convergence
Issue or Number:5
Record Number:CaltechAUTHORS:CHUsiamjco06
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:CHUsiamjco06
Alternative URL:http://dx.doi.org/10.1137/050641193
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6854
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:29 Dec 2006
Last Modified:26 Dec 2012 09:25

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