Central local discontinuous galerkin methods on overlapping cells for diffusion equations
School of Mathematics, Georgia
Institute of Technology, Atlanta, 30332-0160 GA, USA. email@example.com .
2 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. firstname.lastname@example.org
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. email@example.com
4 Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China. firstname.lastname@example.org
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