LOCAL ANALYSIS OF THE FULLY DISCRETE LOCAL DISCONTINUOUS GALERKIN METHOD FOR THE TIME-DEPENDENT SINGULARLY PERTURBED PROBLEM  

作　　者：Yao Cheng Qiang Zhang 

机构地区：[1]Department of Mathematics, Nanjing University, Nanjing 210093, Jiangsu Province, China

出　　处：《Journal of Computational Mathematics》2017年第3期265-288,共24页计算数学（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.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.

关 键 词：Local analysis Runge-Kutta method Local discontinuous Galerkin method Singularly perturbed problem Boundary layer 

分 类 号：O[理学]