Data smoothing technique using finite elements and Sobolev norm.
Data smoothing technique using finite elements and Sobolev norm.
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使用有限元和 Sobolev 范数的数据平滑技术。
DOI：
10.1299/kikaia.54.1354
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
G. Yagawa
中科院分区：
文献类型：
--
作者：
N. Soneda;Shinobu Yoshihara;A. Yoshioka;G. Yagawa
本文介绍了一种新的数据平滑技术的基础上修改的最小二乘法，使用有限元。为了平滑地插值离散数据，通常使用与多项式或样条函数相结合的最小二乘法。然而，这些方法经常引起近似函数的振荡，并且不太适合计算这些函数的导数。为了避免这种振荡，我们提出了一种新的数据平滑技术，使用有限元，其中Sobolev范数最小化。该方法不仅考虑了数据的光滑性，而且考虑了一阶导数的光滑性。本方法适用于一维以及二维问题，其精度和收敛性证明。
This paper describes a new data smoothing technique based on a modified least-squares method using finite elements. To smoothly interpolate discrete data, least-squares methods combined with a polynomial or the spline function are commonly used. However, these methods often cause oscillations in the approximation functions and are not so appropriate to calculate derivatives of those function. In order to avoid such oscillations, we propose a new data smoothing technique using finite elements, where the Sobolev norm is minimized. This method takes into account not only the smoothness of the data but also that of the first-order derivative. The present method is applied to one-dimensional as well as two-dimensional problems, and its accuracy and convergency are demonstrated.