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Macro-element Hierarchical Riesz Bases

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Mathematical Methods for Curves and Surfaces (MMCS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8177))

Abstract

We show that a nested sequence of C r macro-element spline spaces on quasi-uniform triangulations gives rise to hierarchical Riesz bases of Sobolev spaces H s(Ω), \(1<s<r+\frac{3}{2}\), and \(H^s_0(\Omega)\), \(1<s<\sigma+\frac{3}{2}\), \(s\notin\mathbb{Z}+\frac{1}{2}\), as soon as there is a nested sequence of Lagrange interpolation sets with uniformly local and bounded basis functions, and, in case of \(H^s_0(\Omega)\), the nodal interpolation operators associated with the macro-element spaces are boundary conforming of order σ. In addition, we provide a brief review of the existing constructions of C 1 Largange type hierarchical bases.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow, G1 1XH, Scotland

    Oleg Davydov & Wee Ping Yeo

Authors
  1. Oleg Davydov
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  2. Wee Ping Yeo
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Editor information

Editors and Affiliations

  1. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Norway

    Michael Floater

  2. DMA, University of Oslo, P.O.Box 1053, 0316, Blindern, Oslo, Norway

    Tom Lyche

  3. Laboratoire LJK, Université Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France

    Marie-Laurence Mazure

  4. University of Oslo, Norway

    Knut Mørken

  5. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA

    Larry L. Schumaker

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Davydov, O., Yeo, W.P. (2014). Macro-element Hierarchical Riesz Bases. In: Floater, M., Lyche, T., Mazure, ML., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2012. Lecture Notes in Computer Science, vol 8177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54382-1_7

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  • DOI: https://doi.org/10.1007/978-3-642-54382-1_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54381-4

  • Online ISBN: 978-3-642-54382-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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