On very accurate enclosure of the optimal constant in the a priori error estimates for H20-projection
On very accurate enclosure of the optimal constant in the a priori error estimates for H20-projection
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关于 H20 投影的先验误差估计中最优常数的非常准确的包含
DOI：
10.1016/j.cam.2009.12.044
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
M. Nakao
中科院分区：
文献类型：
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作者：
T. Kinoshita;M. Nakao
我们提出了 H02 投影到一维区间多项式空间的建设性先验误差估计。这里，“构造性”表示我们可以获得误差界，其中所有常数都被明确给出或以数值可计算的形式表示。利用勒让德多项式的性质，我们考虑一种方法来确定这些常数尽可能小。使用所提出的技术，可以将最佳常数包含在非常窄的区间内并进行结果验证。此外，还提出了一维有限元 H02 投影的建设性误差估计。这些类型的估计将在非线性四阶椭圆问题解的数值验证以及有限元法或谱法的保证后验误差分析中发挥重要作用（例如，Hashimoto et al. (2006) [2]、Nakao et al. (2008) [3]、Watanabe et al. (2009) [11]）。
We present constructive a priori error estimates for H02-projection into a space of polynomials on a one-dimensional interval. Here, “constructive” indicates that we can obtain the error bounds in which all constants are explicitly given or are represented in a numerically computable form. Using the properties of Legendre polynomials, we consider a method by which to determine these constants to be as small as possible. Using the proposed technique, the optimal constant could be enclosed in a very narrow interval with result verification. Furthermore, constructive error estimates for finite element H02-projection in one dimension are presented. These types of estimates will play an important role in the numerical verification of solutions for nonlinear fourth-order elliptic problems as well as in the guaranteed a posteriori error analysis for the finite element method or the spectral method (e.g. Hashimoto et al. (2006) [2], Nakao et al. (2008) [3], Watanabe et al. (2009) [11]).
泊肃叶流奥尔-索末菲问题的计算机辅助不稳定性证明
DOI：
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发表时间：
2009
期刊：
Z. Angew. Math. Mech. 89
影响因子：
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作者：
Yoshitaka Watanabe;et al.
通讯作者：
et al.