Lagrange四边形单位分解有限元法的最优误差分析

Optimal Error Estimates for Partition of Unity Finite Element Method on Lagrange Rectangle

用构造最优局部逼近空间的方法对Lagrange型四边形单位分解有限元法进行了最优误差分析.单位分解取Lagrange型四边形上的标准双线性基函数,构造了一个特殊的局部多项式逼近空间,给出了具有2阶再生性的Lagrange型四边形单位分解有限元插值格式,从而得到了高于局部逼近阶的最优插值误差.

In this paper, by constructing a optimal local approximation space,we investigate optimal error estimates for partition of unity finite element metbod（PUFEM） on Lagrange rectangle.Using standard base functions defined on bilinear Lagrange rectangle as partition of unity ,a special polynomial local approximation space is established,then PUFEM interpolants with reproducing property of order 2 is constructed. Thereby we derive the optimal error estimates of higher order than the local approximations for PUFEM interpolants.