Uniform Convergence Analysis of the Discontinuous Galerkin Method on Layer-Adapted Meshes for Singularly Perturbed Problem
SHI Jiamin 1LU Zhongshu 1ZHANG Luyi 1LU Sunjia 1CHENG Yao1
作者信息
- 1. School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou 215009,Jiangsu,China
- 折叠
Abstract
This paper concerns a discontinuous Galerkin(DG)method for a one-dimensional singularly perturbed problem which pos-sesses essential characteristic of second order convection-diffusion problem after some simple transformations.We derive an optimal con-vergence of the DG method for eight layer-adapted meshes in a general framework.The convergence rate is valid independent of the small parameter.Furthermore,we establish a sharper L2-error estimate if the true solution has a special regular component.Numerical experi-ments are also given.
Key words
layer-adapted meshes/singularly perturbed problem/uniform convergence/discontinuous Galerkin method引用本文复制引用
基金项目
国家自然科学基金(11801396)
National College Students Innovation and Entrepreneurship Training Project(202210332019Z)
出版年
2023
NETL
NSTL
万方数据