An analysis of some high accuracy finite element methods for hyperbolic problems

被引：7
|
作者：
Zhou, AH [1 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2001年 / 39卷 / 03期
关键词：
conservation laws; finite element; higher accuracy; hyperbolic problems; optimal estimate;
D O I：
10.1137/S0036142999362894
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Some high accuracy finite element methods for hyperbolic problems are studied in this paper. It is proven that over a finite element mesh, the convergence order of linear finite element solutions for both linear and nonlinear equations can be higher than one even if the exact solutions are discontinuous. The theoretical tools for the convergence analysis are some superclose error estimates that are also developed in this paper for nonsmooth solutions.
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页码：1014 / 1028
页数：15
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