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.
Mots-clés : central discontinuous Galerkin method, local discontinuous Galerkin method, overlapping cells, diffusion equation, heat equation, stability, error estimate
@article{M2AN_2011__45_6_1009_0,
author = {Liu, Yingjie and Shu, Chi-Wang and Tadmor, Eitan and Zhang, Mengping},
title = {Central local discontinuous galerkin methods on overlapping cells for diffusion equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1009--1032},
publisher = {EDP-Sciences},
volume = {45},
number = {6},
year = {2011},
doi = {10.1051/m2an/2011007},
mrnumber = {2833171},
zbl = {1269.65098},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2011007/}
}
TY - JOUR AU - Liu, Yingjie AU - Shu, Chi-Wang AU - Tadmor, Eitan AU - Zhang, Mengping TI - Central local discontinuous galerkin methods on overlapping cells for diffusion equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 1009 EP - 1032 VL - 45 IS - 6 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2011007/ DO - 10.1051/m2an/2011007 LA - en ID - M2AN_2011__45_6_1009_0 ER -
%0 Journal Article %A Liu, Yingjie %A Shu, Chi-Wang %A Tadmor, Eitan %A Zhang, Mengping %T Central local discontinuous galerkin methods on overlapping cells for diffusion equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 1009-1032 %V 45 %N 6 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2011007/ %R 10.1051/m2an/2011007 %G en %F M2AN_2011__45_6_1009_0
Liu, Yingjie; Shu, Chi-Wang; Tadmor, Eitan; Zhang, Mengping. Central local discontinuous galerkin methods on overlapping cells for diffusion equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 6, pp. 1009-1032. doi : 10.1051/m2an/2011007. http://archive.numdam.org/articles/10.1051/m2an/2011007/
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