关于Wilson元能量正交性的注记

A note on the energy-orthogonal propties of Wilson elemen

对于二阶椭圆边值问题,Wilson元具有能量正交形函数空间.文中指出在标准基函数下,单元的刚度矩阵为对角块:K=Krc+Kh,其中Krc只和形函数空间的协调部分有关,Kh由非协调部分决定.如果基函数换为和标准基等价的另一组通常的基函数,单元的刚度矩阵仍为对角块,此时Krc只和形函数空间的常应变有关,Kh由高阶模态决定.最后文章还列举了几个常见的具有能量正交形函数空间的矩形元例子.

The Wilson rectanguar element has energy - orthogonal shape function space for the discretization of second order elleptic problem. In this note,we point out that the stiffness matrix of the element are block diagonal：K = Kτc ＋ Kh ,where Kτc corresponds to conforming part of shape function, while Kh is determind by nonconforming part. If replacing the standard basic functions with the other general group, then the stiffness matrix of the element are block diagonal too,where Kτc corresponds to constant strain modes of shape function ;Kh is determind by high modes. In the end of the paper we list some rectanguar elements that have energyorthogonal shape function spaces for the second order elleptic problem.