Identifier: 2009-1
Author(s): Y Cheng and C.-W. Shu
Title: Superconvergence of discontinuous Galerkin and local discontinuous Galerkin schemes for linear hyperbolic and convection diffusion equations in one space dimension
Page count: 36 pp.
Date: 2009-01-27
Abstract:
In this paper, we study the superconvergence property for the discontinuous Galerkin (DG) and the local discontinuous Galerkin (LDG) methods, for solving one-dimensional time dependent linear conservation laws and convection-diffusion equations. We prove su- perconvergence towards a particular pro jection of the exact solution when the upwind flux is used for conservation laws and when the alternating flux is used for convection-diffusion equations. The order of superconvergence for both cases is proved to be k + 3/2 when piecewise P_k polynomials with k ≥ 1 are used. The proof is valid for arbitrary non-uniform regular meshes and for piecewise P_k polynomials with arbitrary k ≥ 1, improving upon the results in [8, 9] in which the proof based on Fourier analysis was given only for uniform meshes and piecewise P_1 polynomials.
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