Burgers方程的非协调特征有限元方法

J4 ›› 2012, Vol. 47 ›› Issue (12): 103-108.

Burgers方程的非协调特征有限元方法

周家全,孙应德,张永胜

洛阳理工学院数理部, 河南洛阳 471023

收稿日期:2011-12-29 出版日期:2012-12-20 发布日期:2012-12-14
作者简介:周家全(1971- ), 男, 副教授, 研究方向为有限元方法研究与应用. Email: lyzhjq@126.comBurgers
基金资助:
国家自然科学基金资助项目(60876014);河南省创新人才基金资助项目(2008HASTIT029);河南省教育厅自然科学研究计划项目(2010B110017,2011B110020);洛阳理工学院自然科学研究项目(2008YZB14, 2011YZ06)

A nonconforming characteristic finite element method for Burgers equations

ZHOU Jia-quan, SUN Ying-de， ZHANG Yong-sheng

Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Luoyang 471023, Henan, China

Received:2011-12-29 Online:2012-12-20 Published:2012-12-14

摘要/Abstract

摘要：

给出了二维Burgers方程一个Crouzeix-Raviart型非协调特征有限元格式, 利用有限元空间的特性, 在不使用传统的投影算子的情况下, 得到了H1模的最优误差估计及其超逼近性质, 并通过构造插值后处理算子得到了超收敛结果。

关键词: Burgers方程;非协调; 特征有限元; 最优误差估计; 超逼近和超收敛

Abstract:

A CrouzeixRaviart type nonconforming characteristic finite element scheme is proposed for 2D Burgers equations. By use of some special properties of the finite element interpolation, and without the projection operator which is a vital tool in the conventional finite element convergence analysis of evolution equations, the optimal H1norm error estimate and some superclose properties are obtained. Also, based on the interpolated postprocessing trick, the global superconvergence is derived.

Key words: Burgers equations; nonconforming; characteristic finite element; the optimal error estimate; supperclose and supperconvergence

周家全,孙应德,张永胜. Burgers方程的非协调特征有限元方法[J]. J4, 2012, 47(12): 103-108.

ZHOU Jia-quan, SUN Ying-de， ZHANG Yong-sheng. A nonconforming characteristic finite element method for Burgers equations[J]. J4, 2012, 47(12): 103-108.

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