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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   

  1. 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.

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   

  1. 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.
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.

MR(2010)主题分类: 

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