中文摘要：

在这份报纸，我们考虑充分分离的本地不连续的 Galerkin 方法，在第三命令前进的明确的 Runge-Kutta 时间被联合的地方。为一个维的时间依赖者有边界层的不可思议地使不安的问题，我们将证明结果的计划具有在本地稳定性的好行为不仅，而且有双 optimal 本地人错误估计。它是说，集中率在空间和时间是最佳的，并且截止子域的宽度也是将近最佳的，如果在各中间的舞台的边界条件以一个合适的方法被给。数字实验也被给。

英文摘要：

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.