完全三次非协调板元的误差估计

ERROR ESTIMATES OF THE COMPLETE CUBIC NONCONFORMING PLATE ELEMENTS

本文考虑以下重调和方程的边值问题:△~2u=f,在G上,u=?u/?n=0,在?G上,其中G为R^2上多边形区域,n为单位外法向量.此问题的变分形式为:找u∈H_0~2(G),使得: α(u,v)=(f,vv)?v∈ _0~~2(G),其中 α(u,v)=∫_G[△u△v+(1-σ)(2u_(x_1x_2)v_(x_1x_2)-u(x_1x_1)v_(x_2x_2)-u_(x_2x_2)v_(x_1x_1))]dx_1dx_2 设τ_h为G的一致正则矩形剖分,h为所有元的最大直径.文[5]中构造了一个完全三次非协调板元,它的形函数为完全三次多项式;

The present paper gives the L^2-error estimate of the complete cubic nonconformingplate elements. Moreover, the L^1-error estimate is obtained after modifying the variation-al form.