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Construction of superconvergent quasi-interpolants using new normalized C2 cubic B-splines
Mathematics and Computers in Simulation ( IF 4.4 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.matcom.2020.07.009
A. Rahouti , A. Serghini , A. Tijini

Abstract In this paper, we use the finite element method to construct a new normalized basis of a univariate C 2 cubic spline space endowed with a specific subdivision of a real interval. Based on the polar forms, we introduce a new representation of the Hermite interpolant of any C 2 piecewise polynomial defined over this subdivision and we construct several superconvergent discrete quasi-interpolants which have an optimal approximation order. This approach is simple and provides an interesting approximation. Numerical results are given to illustrate the theoretical ones.

中文翻译:

使用新的归一化 C2 三次 B 样条构造超收敛准插值

摘要 在本文中,我们使用有限元方法构造了一个单变量C 2 三次样条空间的一个新的归一化基,该空间被赋予了一个实区间的特定细分。基于极坐标形式,我们引入了在该细分上定义的任何 C 2 分段多项式的 Hermite 插值的新表示,并且我们构造了几个具有最佳近似阶数的超收敛离散准插值。这种方法很简单,并提供了一个有趣的近似值。给出了数值结果来说明理论结果。
更新日期:2020-12-01
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