FINITE-ELEMENT INTERPOLATION OF NONSMOOTH FUNCTIONS SATISFYING BOUNDARY-CONDITIONS
FINITE-ELEMENT INTERPOLATION OF NONSMOOTH FUNCTIONS SATISFYING BOUNDARY-CONDITIONS
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DOI：
10.1090/s0025-5718-1990-1011446-7
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发表时间：
1990-04-01
影响因子：
2
通讯作者：
ZHANG, SY
中科院分区：
文献类型：
--
作者：
SCOTT, LR;ZHANG, SY
本文提出了一种修正的拉格朗日型插值算子，用于Sobolev空间中函数的连续分段多项式逼近。为了定义”粗糙”函数的插值器并保持分段多项式边界条件，近似函数在d-或-单纯形上被适当地平均以生成插值算子的节点值。这种平均和插值的组合被证明是一个投影，并证明了投影误差的最佳误差估计。引用
In this paper, we propose a modified Lagrange type interpolation operator to approximate functions in Sobolev spaces by continuous piecewise polynomials. In order to define interpolators for" rough" functions and to preserve piecewise polynomial boundary conditions, the approximated functions are averaged appropriately either on d-or-simplices to generate nodal values for the interpolation operator. This combination of averaging and interpolation is shown to be a projection, and optimal error estimates are proved for the projection error. References