Numerical approximation by discrete interpolating variational splines

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• 作者：A. Kouibia ; ^{kouibia@ugr.es} ; M. Pasadas ^{mpasadas@ugr.es} ; M.L. Rodrí ; guez ^{miguelrg@ugr.es}
• 关键词：Finite element ; Discrete problem ; Variational curve ; Variational surface ; Interpolation ; Spline
• 刊名：Applied Numerical Mathematics
• 出版年：2012
• 期刊代码：8_01689274
• 类别：cp
• 出版时间：September, 2012
• 卷：62
• 期：9
• 页码：1109-1118
• 文件大小：585 K

摘要

An approximation problem of parametric curves and surfaces is studied by a new kind of spline functions from some Lagrange or Hermite data set. We present an interpolation problem by minimizing a functional on a parametric finite element space in order to obtain the new notion of a spline. We call it discrete interpolating variational spline. We show how to compute in practice such spline and we carefully prove a convergence result. To illustrate the generality and practice of this work we give some particular cases and we finish by presenting some numerical and graphical examples.