ESAIM: Mathematical Modelling and Numerical Analysis

Table of Contents - July 2008 - Volume 42 - Issue04

Research Article

L 2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods

Liu, Yingjiea1, Shu, Chi-Wanga2, Tadmor, Eitana3 and Zhang, Mengpinga4

a1 School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA. yingjie@math.gatech.edu

a2 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. shu@dam.brown.edu .

a3 Department of Mathematics, Institute for Physical Science and Technology and Center of Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD 20742, USA. tadmor@cscamm.umd.edu .

a4 Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China. mpzhang@ustc.edu.cn .

Abstract


We prove stability and derive error estimates for the recently introduced central discontinuous Galerkin method, in the context of linear hyperbolic equations with possibly discontinuous solutions. A comparison between the central discontinuous Galerkin method and the regular discontinuous Galerkin method in this context is also made. Numerical experiments are provided to validate the quantitative conclusions from the analysis.

(Received April 17 2007)

(Online publication May 27 2008)

Key Words:

  • Central discontinuous Galerkin method;
  • discontinuous Galerkin method;
  • linear hyperbolic equation;
  • stability;
  • error estimate.

Mathematics Subject Classification:

  • 65M60
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