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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摘要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(the immersed finite elementmetthod),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L^2-模和H^1-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 modi- fied 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 H^1-norm and L^2-norm.

作者王淑燕陈焕贞

机构地区山东师范大学数学科学学院

出处《计算数学》 CSCD 北大核心 2012年第2期125-138,共14页 Mathematica Numerica Sinica

基金国家自然科学基金(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

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

分类号 O241.82 [理学—计算数学]

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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

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