\(C^1\) quadratic macroelements and \(C^1\) orthogonal multiresolution analyses in 2D
type: Item
instance of: scholarly article
title: \(C^1\) quadratic macroelements and \(C^1\) orthogonal multiresolution analyses in 2D
zbMATH Open document ID: 0958.65127
DOI: 10.1016/S0898-1221(00)00143-7
author: N. Delaunay
publication date: 2000-09-20T00:00:00Z
review text: The author presents a way to divide a triangle of an arbitrary regular triangulation \(\Delta\) of a polygon region in \(R^{2}\) into twelve subtriangles. In this refinement \(C^{1}\) quadratic finite elements can be constructed. The paper gives explicit Bézier coefficients of elements in terms of the parameters that describe function and first partial derivative values at vertices and values of the normal derivatives at vertices of subtriangles that lie on the edges of \(\Delta\). The basis and approximation properties of the \(C^{1}\) quadratic spline space under the refined grid partition are found. Finally, the construction of \(C^{1}\) orthogonal scaling functions by using \(C^{1}\) quadratic macroelements is discussed.
reviewed by: Plamen Yalamov
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 1471519
zbMATH Keywords: \(C^{1}\) quadratic macroelement
zbMATH Keywords: generalized vertex spline
zbMATH Keywords: bivariate spline space
zbMATH Keywords: \(C^{1}\) orthogonal multiresolution analysis
zbMATH Keywords: \(C^{1}\) orthogonal scaling functions
zbMATH Keywords: regular triangulation
zbMATH Keywords: finite elements
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1471519