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The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

Authors: Bernardo Cockburn and Chi-Wang ShuAuthors Info & Affiliations
https://doi.org/10.1137/S0036142997316712
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Abstract

In this paper, we study the local discontinuous Galerkin (LDG) methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge--Kutta discontinuous Galerkin (RKDG) methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, high-order formal accuracy, and easy handling of complicated geometries for convection-dominated problems. It is proven that for scalar equations, the LDG methods are L2-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are kth order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.

MSC codes

  1. 65M60
  2. 65M12
  3. 65M15

Keywords

  1. discontinuous finite elements
  2. convection-diffusion problems

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Information & Authors

Information

Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Volume 35 • Issue 6 • January 1998
Pages: 2440 - 2463
DOI: 10.1137/S0036142997316712
ISSN (online): 1095-7170

Copyright

Copyright © 1998 Society for Industrial and Applied Mathematics.

History

Published online: 25 July 2006

MSC codes

  1. 65M60
  2. 65M12
  3. 65M15

Keywords

  1. discontinuous finite elements
  2. convection-diffusion problems

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