TY - JOUR
T1 - Local Analysis of the Fully Discrete Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem
AU - Cheng , Yao
AU - Zhang , Qiang
JO - Journal of Computational Mathematics
VL - 3
SP - 265
EP - 288
PY - 2017
DA - 2017/06
SN - 35
DO - http://doi.org/10.4208/jcm.1605-m2015-0398
UR - https://global-sci.org/intro/article_detail/jcm/9773.html
KW - Local analysis, Runge-Kutta method, Local discontinuous Galerkin method,
Singularly perturbed problem, Boundary layer.
AB - <p style="text-align: justify;">In this paper we consider the fully discrete local discontinuous Galerkin method, where the third order explicit Runge-Kutta time marching is coupled. For the one-dimensional time-dependent singularly perturbed problem with a boundary layer, we shall prove that the resulted scheme is not only of good behavior at the local stability, but also has the double-optimal local error estimate. It is to say, the convergence rate is optimal in both space and time, and the width of the cut-off subdomain is also nearly optimal, if the boundary condition at each intermediate stage is given in a proper way. Numerical experiments are also given.</p>