二阶椭圆型问题混合元法的后处理  

A POST-PROCESSING METHOD FOR THE SECOND ORDER ELLIPTIC PROBLEM IN MIXED FINITE ELEMENT METHOD

作　　者：华冬英[1] 王烈衡[1] 

机构地区：[1]中国科学院数学与系统科学研究院计算数学与科学工程计算研究所

出　　处：《数值计算与计算机应用》2005年第3期177-182,共6页Journal on Numerical Methods and Computer Applications

摘　　要：本文讨论了一维、二维情形的二阶椭圆型微分方程模型问题的混合元法后处理.利用最原始、最简单的Taylor展式逼近的思想,对原问题的最低次混合元解作后处理,得到关于数值解的更高阶精度的逼近.这样的后处理方法不提高原逼近多项式的次数,即仍用一次多项式逼近,后处理过程也几乎不占额外的工作量,而且数值实验表明应用这种方法所得的L2范数误差优于Bramble,Xu中的结果.In this paper, we consider the model problem of the second order elliptic differential equation{-△u=f in Ω,u=0 on aΩ.Arnold, Brezziand Bramble, Xuet.al, have done some work on this topic. We use the most original and simplest idea, that is to say, the Taylor expansion approximation to deal with the lowest-order solution of the mixed finite element method and obtain more accurate numerical results. In this method, the degree of the approximation polynomials are not raised and almost no extra workload is needed. Moreover, numerical experiments show that the L^2-norm error of the displacement u is superior to that of Bramble, Xu＇s.

关 键 词：混合元法 后处理 二阶椭圆型微分方程 后处理方法 椭圆型问题 多项式逼近 TAYLOR展式 模型问题 混合元解 高阶精度 

分 类 号：O241.8[理学—计算数学]