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Central local discontinuous Galerkin methods on overlapping cells for diffusion equations. (English) Zbl 1269.65098
Summary: 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.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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