ON EXPLICIT BOUNDS IN THE ERROR FOR THE $ mathrm{H_o^1} $-PROJECTION INTO PIECEWISE POLYNOMIAL SPACES
ON EXPLICIT BOUNDS IN THE ERROR FOR THE $ mathrm{H_o^1} $-PROJECTION INTO PIECEWISE POLYNOMIAL SPACES
复制标题
关于 $ mathrm{H_o^1} $ 投影到分段多项式空间中的错误的显式界限
DOI：
10.5109/13484
复制
发表时间：
1999
期刊：
影响因子：
--
通讯作者：
N. Yamamoto
中科院分区：
文献类型：
--
作者：
S. Kimura;N. Yamamoto
在椭圆型方程的数值验证方法中，有限元方法的近似误差估计中出现的常数值起着重要作用（Nakao and Yamamoto（1998），Yamamoto and Nakao（1995）等）。为了在计算机上有效地实现验证算法，有必要尽可能接近它们的最佳值来估计这些常数。在Nakao，Yamamoto和Kimura（1998）中，导出了二次元素的最佳常数以及三次元素的接近最佳值。本文建立了一种计算任意次分段多项式逼近常数的方法，并给出了计算所得常数与最优值之差的界。
The values of constants appearing in error estimates of approximations by finite element methods play an important role in numerical verification methods for elliptic equations (Nakao and Yamamoto(1998),Yamamoto and Nakao(1995) , etc.).For efficient implementation of the verification algorithms on computers, it is necessary that these constants can be estimated as close as possible to their optimal values. In Nakao,Yamamoto and Kimura(1998), the optimal constant was derived for quadratic elements as well as a nearly optimal value for cubic elements. In this paper, we establish a method to calculate the values of constants for approximation by piecewise polynomials of arbitrary degree and to give bounds on the difference between the constants so calculated and optimal values.