TY - JOUR T1 - Error Estimate on a Fully Discrete Local Discontinuous Galerkin Method for Linear Convection-Diffusion Problem JO - Journal of Computational Mathematics VL - 3 SP - 283 EP - 307 PY - 2013 DA - 2013/06 SN - 31 DO - http://doi.org/10.4208/jcm.1212-m4174 UR - https://global-sci.org/intro/article_detail/jcm/9735.html KW - Runge-Kutta, Local discontinuous Galerkin method, Convection-diffusion equation, Error estimate. AB -

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.