关于特征值问题有限元方法研究的一个说法  

A Statement about Finite Element Methods of Eigenvalue Problems

作　　者：李琴[1] 

机构地区：[1]北京工商大学理学院,北京100048

出　　处：《数学的实践与认识》2014年第10期294-300,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11101414);973项目(2011CB309703)

摘　　要：受林群的微积分哲学公式((相对真理)/(绝对真理)=0.9)的启示,总结了近些年来关于特征值问题有限元方法的研究,并发现其背后同样隐藏着该哲学公式,换句话说,所追求的是特征值问题的有限元数值解和真解的零距离,其实就是追求真解的过程,要经多道(即0.9,0.99,0.999,…),再将比例,即(数值解)/(真解),提到1.Inspired by Qun Lin＇s philosophical formula of Calculus,Relative truth/Absolute truth=0.9,we review our recent research for finite element methods of eigenvalue problems and find that there also hides this philosophical formula behind.That is to say,in our research,we usually pursue that numerical solutions by finite element methods are convergent to the corresponding true solutions,whereas we practically go through multiple processes（i.e.0.9,0.99,0.999,…） to pursue true solutions such that the ratio of numerical solutions and true solutions is closer and closer to 1.

关 键 词：微积分哲学公式 相对真理 绝对真理=0 9 特征值问题 有限元方法 

分 类 号：O241.82[理学—计算数学]