Sobolev方程的扩展混合体积元方法

J4 ›› 2012, Vol. 47 ›› Issue (6): 34-39.

Sobolev方程的扩展混合体积元方法

李娜,高夫征*,张天德

山东大学数学学院, 山东济南 250100

收稿日期:2011-10-11 出版日期:2012-06-20 发布日期:2012-06-26
通讯作者: 高夫征 (1973- ), 男,博士,副教授, 研究方向为偏微分方程数值解法. Email:fzgao@sdu.edu.cn
作者简介:李娜(1987- ), 女, 硕士研究生,研究方向为偏微分方程数值解法. Email:dajiena2002@163.com
基金资助:
山东省中青年科学家科研奖励基金资助项目(BS2009HZ015)

An expanded mixed covolume method for Sobolev equations

LI Na, GAO Fu-zheng*, ZHANG Tian-de

School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Received:2011-10-11 Online:2012-06-20 Published:2012-06-26

摘要/Abstract

摘要：

基于最低次R-T混合有限元空间,提出了求解一类 Sobolev 方程的扩展混合体积元格式,利用微分方程先验误差估计技巧,给出了扩展混合体积元解的误差分析,分别得到了扩展混合体积元半离散格式和全离散格式解的次优阶L²误差估计, 数值试验很好地验证了这一点。

关键词: Sobolev 方程; 扩展混合体积元; 误差估计; 数值试验

Abstract:

Based on the lowest order RaviartThomas mixed element space, an expanded mixed covolume method forsolving a class of Sobolev equations is presented. Making use of priori error estimate techniques, the suboptimal L²error estimates for the semidiscrete and fullydiscrete schemes are obtained. Also some numerical results are given to verify our analysis for the schemes.

Key words: Sobolev equation; expanded mixed covolume method; error estimate;numerical experiments

李娜,高夫征*,张天德. Sobolev方程的扩展混合体积元方法[J]. J4, 2012, 47(6): 34-39.

LI Na, GAO Fu-zheng*, ZHANG Tian-de. An expanded mixed covolume method for Sobolev equations[J]. J4, 2012, 47(6): 34-39.

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