Nodal superconvergence of the local discontinuous Galerkin method for singularly perturbed problems

被引：5

作者：

Zhu, Huiqing ^{[1
]}

Celiker, Fatih ^{[2
]}

机构：

[1] Univ Southern Mississippi, Dept Math, Hattiesburg, MS 39406 USA

[2] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2018年 / 330卷

基金：

美国国家科学基金会;

关键词：

Local discontinuous Galerkin method; Singularly perturbed problems; Local error estimates; Superconvergence; CONVECTION-DIFFUSION PROBLEMS; FINITE-ELEMENT SUPERCONVERGENCE; UNIFORM SUPERCONVERGENCE; HP-VERSION; LDG METHOD; DISCRETIZATION; APPROXIMATIONS;

D O I：

10.1016/j.cam.2017.07.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a superconvergence of order (In N/N)(2k+1) for the numerical traces of the LDG approximation to a one dimensional singularly perturbed convection diffusion reaction problem is proved. The LDG method is applied on a Shishkin mesh with 2N elements, and we use polynomials of degree at most k on each element. This result puts the numerical finding reported in Xie and Zhang (2007), Xie et al. (2009) on firm mathematical ground. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：95 / 116

页数：22

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