Stokes问题的集中质量非协调有限元法

主要讨论了一类Stokes问题的质量集中非协调有限元方法———半离散情形 .首先给出了所讨论问题的质量集中非协调Galerkin有限元方法的离散格式 ;其次对所讨论问题的解与其所给出的离散问题的解之间的误差进行了分析研究 ;最后利用Stokes投影算子的性质 ,得到了L2 模和能量模方面的一些误差估计     

SUPERCONVERGENCE ANALYSIS OF A NONCONFORMING TRIANGULAR ELEMENT ON ANISOTROPIC MESHES

The class of anisotropic meshes we conceived abandons the regular assumption. Some distinct properties of Carey＇s element are used to deal with the superconvergence for a class of two- dimensional second-order elliptic boundary value problems on anisotropic meshes. The optimal results are obtained and numerical examples are given to confirm our theoretical analysis.     

特征值问题强间断非协调元逼近

本女给出了四阶特征值问题强间断非协调有限元，Ｍｏｒｌｅｙ元及广义协调元的逼近的统一形式，得到了最优的误差估计     

Stokes方程非协调有限元逼近的快速迭代过程

对Ｓｔｏｋｅｓ方程的非协调有限元逼近提出了一个快速计算方法。基本思想是把原来的对称不定问题的计算转化为对称正定问题的计算,这个对称正定问题将由共轭斜量法求解,而共轭斜量法中每步迭代的计算需要求解带正定矩阵的线性代数方程组,采用亏量校正算法来近似求解,证明了算法具有与网格步长无关的小于１的收敛率。     

ACCURACY ANALYSIS OF 12-PARAMETER RECTANGULAR PLATE ELEMENTS WITH GEOMETRIC SYMMETRY

1. IntroductionAs for triangular thin plate element, it is observed in practice that the numerical accuxacyof the two unconventional plate elemellts, namely, the nine parameter quasi--conforming[1] andgeneralized conforming elements[2], is better than that of the usual Zienkiewicz's elemellt andSpecht's element[3], although all these elements have the same asymptotical rate of convergenceO(h) in the energy norm. How to explain the discrepancy between the theoretical analysis andnumerical comp…