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Hierarchical Riesz Bases for Hs(Omega), 1 < s < 5/2

Davydov, Oleg and Stevenson, Rob (2005) Hierarchical Riesz Bases for Hs(Omega), 1 < s < 5/2. Constructive Approximation, 22 (3). pp. 365-394. ISSN 0176-4276

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Abstract

On arbitrary polygonal domains $Omega subset RR^2$, we construct $C^1$ hierarchical Riesz bases for Sobolev spaces $H^s(Omega)$. In contrast to an earlier construction by Dahmen, Oswald, and Shi (1994), our bases will be of Lagrange instead of Hermite type, by which we extend the range of stability from $s in (2,frac{5}{2})$ to $s in (1,frac{5}{2})$. Since the latter range includes $s=2$, with respect to the present basis, the stiffness matrices of fourth-order elliptic problems are uniformly well-conditioned.

Item type: Article
ID code: 4543
Keywords: hierarchical bases, splines, c1 finite elements, probability, mathematics, Probabilities. Mathematical statistics, Mathematics, Computational Mathematics, Analysis, Mathematics(all)
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Strathprints Administrator
Date Deposited: 01 Nov 2007
Last modified: 15 Apr 2015 09:24
Related URLs:
URI: http://strathprints.strath.ac.uk/id/eprint/4543

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