平面弹性力学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 Plane Elasticity Problems

作　　者：安静[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：《数学物理学报（A辑）》2011年第5期1253-1265,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(10871022;11061009);河北省自然科学基金(A2010001663)资助

摘　　要：该文研究平面弹性力学问题基于泡函数的稳定化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18N_p个自由度(其中N_p是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 plane elasticity problems 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 that of the stabilized second order mixed finite it can save 18Np freedom degrees （where Np is eliminated all bubble functions is the same as element formulation with bubble functions, but the number of vertices of triangularization）.

关 键 词：平面弹性力学问题 混合有限元格式 简化的稳定化格式 误差估计. 

分 类 号：O241.4[理学—计算数学]