板的低阶间断与连续有限元法统一分析

基于Reissner-Mindlin板问题的间断Galerkin有限元逼近, 建立了一个对挠度空间和角位移空间取连续或间断元都适用的低阶有限元离散格式. 取剪切力空间为分片常数元, 挠度空间和角位移空间无论取间断元还是连续元, 格式都是一致稳定的, 并给出了H¹范数估计及L²范数估计. 作为应用,对几类低阶有限元空间讨论. 结果表明, 该格式对常见的低阶有限元空间都适用, 并且若至少有一个元连续时, 该格式需要的空间比1,2]中的都要简单.  

UNIFIED ANALYSIS OF LOW ORDER DISCONTINUOUS AND CONTINUOUS FINITE ELEMENT METHODS FOR THE REISSNER-MINDLIN PLATE

Based on the discontinuous Galerkin method, a unified low-order formulation, which can apply to both continuous and discontinuous transverse displacement and rotation finite element spaces, is proposed for the Reissner-Mindlin plate problem. Piecewise constants are used to approximate the shear stress vectors. This scheme is stable, whether continuous or discontinuous finite element spaces are used to approximate the transverse displacement and the rotation. And is convergent uniformly with respect to thickness. The optimal H¹ and L² error bounds are proven. Finally, several low order finite element spaces are given for different cases. It is proved that most low order finite element spaces can be applied to our scheme. If there is at least one variable continuous, the spaces needed in our method are simpler than those of 1, 2].