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overlapping cells

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Central local discontinuous galerkin methods on overlapping cells for diffusion equations
Yingjie Liu, Chi-Wang Shu, Eitan Tadmor, Mengping Zhang
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 45 / Issue 6 / November 2011

Published online by Cambridge University Press:

10 June 2011, pp. 1009-1032

Print publication:

November 2011
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In this paper we present two versions of the central localdiscontinuous Galerkin (LDG) method on overlapping cellsfor solving diffusion equations, and provide theirstability analysis and error estimates for the linear heat equation.A comparisonbetween the traditional LDG method ona single mesh and the two versions of the central LDGmethod on overlapping cells is also made.Numerical experiments are provided to validate the quantitativeconclusions from the analysis and to support conclusions forgeneral polynomial degrees.