位移障碍下四阶变分不等式问题的非协调有限元一般误差估计式

GENERAL ERROR ESTIMATES OF THE NONCONFORMING FINITE ELEMENTS FOR A FOURTH ORDER VARIATIONAL INEQUALITY WITH DISPLACEMENT OBSTACLE

1.引言 关于二阶变分不等式问题的非协调有限元逼近已有大量研究[1-5].但是,对于四阶变分不等式的研究相对而言较少[6-7].[8,9,10]给出了位移障碍问题的非协调有限元,包括C0元(如Zienkiewicz元及Adini元)和非C0元(如Morley元及De Veubeke元)逼近的理论分析及最优误差估计.经过仔细分析发现,其成功的关键技巧是充分利用上述单元的一个共同性质:即有限元插值函数在单元顶点连续.但是,对于那些不满足这一性质的单元,如Bergan能量正交元[11]、双参数能量正交元[12]等,[8,9,10]提供的方法是行不通的.

This paper gives general error estimates of nonconforming finite element approximation to a fourth order variational inequality with displacement obstacle. The optimal error estimate is obtained. The present method is simple, effective and can be regarded as a general framework applicable to almost known non-conforming finite elements.