Geodesic
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

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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.

DOI : 10.1051/m2an/2011007
Classification : 65M60
Keywords: central discontinuous Galerkin method, local discontinuous Galerkin method, overlapping cells, diffusion equation, heat equation, stability, error estimate 
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     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},
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     year = {2011},
     doi = {10.1051/m2an/2011007},
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     zbl = {1269.65098},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011007/}
}
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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

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