Error Estimate on a Fully Discrete Local Discontinuous Galerkin Method for Linear Convection-Diffusion Problem
Year: 2013
Journal of Computational Mathematics, Vol. 31 (2013), Iss. 3 : pp. 283–307
Abstract
In this paper we present the error estimate for the fully discrete local discontinuous Galerkin algorithm to solve the linear convection-diffusion equation with Dirichlet boundary condition in one dimension. The time is advanced by the third order explicit total variation diminishing Runge-Kutta method under the reasonable temporal-spatial condition as general. The optimal error estimate in both space and time is obtained by aid of the energy technique, if we set the numerical flux and the intermediate boundary condition properly.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1212-m4174
Journal of Computational Mathematics, Vol. 31 (2013), Iss. 3 : pp. 283–307
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Runge-Kutta Local discontinuous Galerkin method Convection-diffusion equation Error estimate.