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

• 来源期刊: 计算数学（英文版）
• 关键词: Local analysis Runge-Kutta method Local discontinuous Galerkin method Singularly perturbed problem Boundary layer
• 年，卷（期）: 2017,（3）
• 页码范围: 265-288
• 页数: 24页
• 语种: 英文
• DOI: 10.4208/jcm.1605-m2015-0398

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.