板振动问题Ciarlet-Raviart混合有限元渐近展开式与Richardson外推  

THE ASYMPTOTIC EXPANSIONS AND THE RICHARDSON EXTRAPOLATION OF THE CIARLET-RAVIART MIXED FINITE ELEMENT METHOD FOR VIBRATIONS PROBLEM OF PLATE

作　　者：杨一都[1] 

机构地区：[1]贵州师范大学数学与计算机科学学院,贵阳550001

出　　处：《高等学校计算数学学报》2008年第3期201-212,共12页Numerical Mathematics A Journal of Chinese Universities

基　　金：贵州省高层次人才科研条件特助经费资助项目

摘　　要：1引言Richardson外推是数值计算各个方面广泛使用的一种高效算法,它的理论基础是渐近展开式.1983年文对三角形网格首先证明了二阶椭圆问题协调有限元渐近展开式,这以后有限元外推迅速发展成一个国际性研究课题,文[5],[7]对有限元外推作了系统。In this paper the Richardson extrapolation of the Ciarlet-Raviart mixed finite element method for eigenvalue problem in linear plate is discussed. And the asymptotically expansions of the Ciarlet-Raviart mixed finite element eigenvalues and eigenfunctions for the clamped plate with bilinear finite element space on the uniform rectangular mesh and for the simply supported plate with linear finite element space on the three-directional triangulations meshes are given. These expansions are then applied to obtain two extrapolation schemes. Theoretical analysis and numerical experiments show that the constructed extrapolation schemes are effective.

关 键 词：板振动 Ciarlet-Raviart 有限元 渐近展开式 RICHARDSON外推 

分 类 号：O241.82[理学—计算数学]