Local Analysis of Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem

In this paper we will present the local stability analysis and local error estimate for the local discontinuous Galerkin (LDG)method, when solving the time-dependent singularly perturbed problems in one dimensional spacewith a stationary outflow boundary layer. Based on a general framework on the local stability, we obtain the optimal error estimate out of the local subdomain, which is nearby the outflow boundary point and has the width of O(h log(1/h)), for the semi-discrete LDG scheme and the fully-discrete LDG scheme with the second order explicit Runge–Kutta time-marching. Here h is the maximum mesh length. The numerical experiments are given also.