Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection - diffusion and KdV equations

被引：113

作者：

Xu, Yan ^{[1
]}

Shu, Chi-Wang

机构：

[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[2] Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2007年 / 196卷 / 37-40期

基金：

美国国家科学基金会;

关键词：

local discontinuous Galerkin method; error estimate; KdV equation; Nonlinear convection-diffusion equation; FINITE-ELEMENT-METHOD; CONSERVATION-LAWS; SMOOTH SOLUTIONS;

D O I：

10.1016/j.cma.2006.10.043

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we provide L-2 error estimates for the semi-discrete local discontinuous Galerkin methods for nonlinear convection-diffusion equations and KdV equations with smooth solutions. The main technical difficulty is the control of the inter-element jump terms which arise because of the nonlinearity of the PDEs and the discontinuous nature of the numerical method. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：3805 / 3822

页数：18

共 37 条

[1]

[Anonymous], 1975, FINITE ELEMENT METHO

[2] Unified analysis of discontinuous Galerkin methods for elliptic problems [J].