关于四次非协调板元的收敛性

ON THE CONVERGENCE OF THE FOURTH DEGREE NONCONFORMING PLATE ELEMENT

讨论一种三角剖分下的四次非协调元，它是Ｃ０元，在每个单元上的形函数是一个完全四次多项式，由单元三顶点处的函数值与一阶偏导数值，及三边中点处的函数值与法向导数值所决定。将此有限元用于薄板弯曲问题，得出了关于能量模以及Ｌ２模的收敛阶估计。与已知为收敛的Ｍｏｒｌｅｙ元相比，其相应的收敛性结果更强。

A kind of fourth degree nonconforming triangular plate element,belonging to C 0,is discussed in this paper.The shape function in each element is a complete fourth degree polynomial,which is made by the value and the values of partial derivative at each vertex,and the value and the normal derivative at the midpoint of each face. By applying this finite element to plate bending problem,the convergence rates of stresses and displacements are obtained. In comparison with the Morley's element ,the convergence results are stronger.