基于Crouzeix-Raviart元的界面浸入有限元方法及其收敛性分析

doi:10.12286/jssx.2012.2.125

计算数学 ›› 2012, Vol. 34 ›› Issue (2): 125-138.DOI: 10.12286/jssx.2012.2.125

基于Crouzeix-Raviart元的界面浸入有限元方法及其收敛性分析

王淑燕, 陈焕贞

山东师范大学数学科学学院, 济南 250014

收稿日期:2010-06-22 出版日期:2012-05-15 发布日期:2012-05-20
通讯作者: 陈焕贞
基金资助:
国家自然科学基金(10271068,10971254), 山东省自然科学基金(ZR2009AZ003),山东省优秀中青年科学家科研奖励基金(2008BS01008)资助项目.

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王淑燕, 陈焕贞. 基于Crouzeix-Raviart元的界面浸入有限元方法及其收敛性分析[J]. 计算数学, 2012, 34(2): 125-138.

Wang Shuyan, Chen Huanzhen. AN IMMERSED FINITE ELEMENT METHOD BASED ON CROUZEIX-RAVIART ELEMENTS[J]. Mathematica Numerica Sinica, 2012, 34(2): 125-138.

AN IMMERSED FINITE ELEMENT METHOD BASED ON CROUZEIX-RAVIART ELEMENTS

Wang Shuyan, Chen Huanzhen

School of Mathematical Sciences, Shandong Normal University, Jinan, Shandong 250014, China

Received:2010-06-22 Online:2012-05-15 Published:2012-05-20

本文对具间断系数的二阶椭圆界面问题提出一种浸入有限元方法(theimmersed finite element method), 即在界面单元上采用依赖于界面的线性多项式空间离散, 而在非界面单元上采用Crouzeix-Raviart非协调元离散. 论证表明, 该方法具有对界面问题解的最优L²-模和H¹-模收敛精度.

关键词： 二阶椭圆界面问题, 浸入有限元, Crouzeix-Raviart 元, 最优误差估计

In this paper we present an immersed finite element method to solve numerically second order elliptic interface problems. The characteristics of the method is to prescribe a modified linear finite element space on each interface element in order to enforce the flux jump condition on the smooth interface, and a Crouzeix-Raviart non-conforming element on each non-interface element. Optimal-order error estimates are derived in the broken H¹?norm and L²?norm.

Key words: second order elliptic interface problems, the immersed finite element, Crouzeix- Raviart elements, optimal-order error estimates

MR(2010)主题分类:

65N15
65N30

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摘要

基于Crouzeix-Raviart元的界面浸入有限元方法及其收敛性分析

AN IMMERSED FINITE ELEMENT METHOD BASED ON CROUZEIX-RAVIART ELEMENTS

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