Convergence of an explicit upwind finite element method to multi-dimensional conservation laws

被引：0

作者：

Xu, JC

Ying, LA

机构：

[1] Penn State Univ, Ctr Computat Math & Applicat, University Pk, PA 16802 USA

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[3] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2001年 / 19卷 / 01期

关键词：

conservation law; finite element method; convergence;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An explicit upwind finite element method is given for the numerical computation to multi-dimensional scalar conservation laws. It is proved that this scheme is consistent to the equation and monotone, and the approximate solution satisfies discrete entropy inequality. To guarantee the limit of approximate solutions to be a measure valued solution, we prove an energy estimate. Then the L-p strong convergence of this scheme is proved.

引用

页码：87 / 100

页数：14

共 18 条

[1]

CIARLET P. G., 1978, The Finite Element Method for Elliptic Problems

[2]

COCKBURN B, 1994, MATH COMPUT, V63, P77, DOI 10.1090/S0025-5718-1994-1240657-4

[3] TVB RUNGE-KUTTA LOCAL PROJECTION DISCONTINUOUS GALERKIN FINITE-ELEMENT METHOD FOR CONSERVATION-LAWS .2. GENERAL FRAMEWORK [J].