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Central local discontinuous galerkin methods on overlapping cells for diffusion equations

Published online by Cambridge University Press:  10 June 2011

Yingjie Liu ,
Chi-Wang Shu ,
Eitan Tadmor  and
Mengping Zhang
Yingjie Liu
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, 30332-0160 GA, USA. yingjie@math.gatech.edu .
Chi-Wang Shu
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. shu@dam.brown.edu
Eitan Tadmor
Affiliation:
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
Mengping Zhang
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China. mpzhang@ustc.edu.cn
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Abstract

In this paper we present two versions of the central local discontinuous Galerkin (LDG) method on overlapping cells for solving diffusion equations, and provide their stability analysis and error estimates for the linear heat equation. A comparison between the traditional LDG method on a single mesh and the two versions of the central LDG method on overlapping cells is also made. Numerical experiments are provided to validate the quantitative conclusions from the analysis and to support conclusions for general polynomial degrees.

Keywords

Central discontinuous Galerkin methodlocal discontinuous Galerkin methodoverlapping cellsdiffusion equationheat equationstabilityerror estimate
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 6 , November 2011 , pp. 1009 - 1032
Copyright
© EDP Sciences, SMAI, 2011

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