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Argyris type quasi-interpolation of optimal approximation order
Computer Aided Geometric Design ( IF 1.5 ) Pub Date : 2020-04-10 , DOI: 10.1016/j.cagd.2020.101836
Jan Grošelj

The paper investigates a quasi-interpolation framework for the construction of operators that provide approximations for bivariate functions from the space of Argyris macro-element splines on a general triangulation. An operator of such type is determined by local approximation operators that produce quintic polynomials and are naturally associated with vertices and triangles of the triangulation. The quasi-interpolant resembles the properties of the standard Argyris interpolant, especially in the determination of data corresponding to the vertices of the triangulation. The main difference is in the definition of the cross-boundary derivatives, where a novel approach with degree raising is used to eliminate the need for additional interpolation of derivatives at the edges. Despite reduction in degrees of freedom, a suitable choice of local approximation operators ensures that the quasi-interpolation operator has quintic precision and is of optimal approximation order. To demonstrate the usability of the presented approach, three approximation methods are derived based on local Hermite and Lagrange interpolation and least square fitting.



中文翻译:

最佳逼近阶的Argyris型拟插值

本文研究了用于构造算子的拟插值框架,该算子在一般三角剖分上的Argyris宏元素样条空间中提供了二元函数的近似值。这种类型的算子由产生五次多项式并自然与三角剖分的顶点和三角形关联的局部逼近算子确定。准插值类似于标准Argyris插值的属性,尤其是在确定与三角剖分的顶点对应的数据时。主要区别在于跨边界导数的定义,其中使用了一种提高度数的新方法来消除对边缘处导数进行附加插值的需要。尽管自由度有所降低,的局部近似算确保一个合适的选择,所述拟插值运营商具有五次精度和是最佳逼近量级。为了证明所提出方法的可用性,基于局部Hermite和Lagrange插值以及最小二乘拟合推导了三种近似方法。

更新日期:2020-04-10
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