Identifier: 2008-10
Author(s): Y. Cheng and C.-W. Shu
Title: Superconvergence of Local Discontinuous Galerkin Methods for Convection-Diffusion Equations
Page count: 48 pp.
Abstract:
In this paper, we study the convergence behavior of the local discontin- uous Galerkin (LDG) methods when applied to time dependent convection- diffusion equations. We show that the LDG solution will be superconvergent towards a particular pro jection of the exact solution, if this pro jection is carefully chosen based on the convection and diffusion fluxes. The order is observed to be at least k + 2 when piecewise P k polynomials are used. Moreover, the numerical traces for the solution are also superconvergent, sometimes, of higher order. This is a continuation of our previous work [6], in which superconvergence of DG schemes for convection equations is discussed.
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