| Issue |
ESAIM: M2AN
Volume 45, Number 6, November-December 2011
|
|
|---|---|---|
| Page(s) | 1009 - 1032 | |
| DOI | https://doi.org/10.1051/m2an/2011007 | |
| Published online | 10 June 2011 | |
Central local discontinuous galerkin methods on overlapping cells for diffusion equations
1
School of Mathematics, Georgia
Institute of Technology, Atlanta, 30332-0160 GA, USA. yingjie@math.gatech.edu .
2
Division of Applied
Mathematics, Brown University, Providence, RI 02912, USA. shu@dam.brown.edu
3
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
4
Department of
Mathematics, University of Science and Technology of China, Hefei,
Anhui 230026, P.R. China. mpzhang@ustc.edu.cn
Received:
9
December
2009
Revised:
6
January
2011
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.
Mathematics Subject Classification: 65M60
Key words: Central discontinuous Galerkin method / local discontinuous Galerkin method / overlapping cells / diffusion equation / heat equation / stability / error estimate
© EDP Sciences, SMAI, 2011
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