Local Discontinuous Galerkin Finite Element Method and Error Estimates for One Class of Sobolev Equation

被引：52

作者：

Gao, Fuzheng ^{[1
,2
]}

Qiu, Jianxian ^{[1
]}

Zhang, Qiang ^{[1
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

[2] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2009年 / 41卷 / 03期

关键词：

Sobolev equation; Local discontinuous Galerkin method; Fully-discrete; Stability analysis; Error estimate; CONSERVATION-LAWS; NUMERICAL-SOLUTION; CONVECTION; DIFFUSION; SCHEMES; SYSTEMS;

D O I：

10.1007/s10915-009-9308-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present a numerical scheme based on the local discontinuous Galerkin (LDG) finite element method for one class of Sobolev equations, for example, generalized equal width Burgers equation. The proposed scheme will be proved to have good numerical stability and high order accuracy for arbitrary nonlinear convection flux, when time variable is continuous. Also an optimal error estimate is obtained for the fully discrete scheme, when time is discreted by the second order explicit total variation diminishing (TVD) Runge-Kutta time-marching. Finally some numerical results are given to verify our analysis for the scheme.

引用

页码：436 / 460

页数：25

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