二阶椭圆问题基于泡函数的简化的稳定化二阶混合有限元格式  

A SIMPLIFIED AND STABILIZED SECOND ORDER MIXED FINITE ELEMENT FORMULATION BASED ON BUBBLE FUNCTIONS FOR SECOND-ORDER ELLIPTIC EQUATIONS

作　　者：张贵明[1] 孙萍[1] 罗振东[2] 

机构地区：[1]贵州师范大学数学与计算机科学学院,贵阳550001 [2]华北电力大学数理学院,北京102206

出　　处：《计算数学》2010年第3期327-336,共10页Mathematica Numerica Sinica

基　　金：国家自然科学基金(批准号:10871022);河北省自然科学基金(批准号:A2010001663)资助项目

摘　　要：本文研究二阶椭圆方程基于泡函数的稳定化的二阶混合有限元格式，通过消去泡函数导出一种自由度很少的简化的稳定化的二阶混合有限元格式，误差分析表明消去泡函数的简化格式与带有泡函数的格式具有相同的精度而可以节省6Np个自由度（其中Np三角形剖分中的顶点数目）．In this paper, a stabilized second order mixed finite element formulation based on bubble functions for second-order elliptic equations is studied, and a simplified second order mixed finite element formulation with less freedom degrees is obtained by eliminating all bubble functions. It is shown by analyzing error that the convergence of the simplified and stabilized second order mixed finite element formulation eliminated all bubble functions is the same as that of the stabilized second order mixed finite element formulation with bubble functions, but it can save 6Np freedom degrees （where Np is the number of vertices of triangulaxization）.

关 键 词：二阶椭圆方程 混合有限元格式 简化的稳定化格式 误差估计 

分 类 号：O241.82[理学—计算数学]