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. 365394. ISSN 01764276
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Official URL: https://doi.org/10.1007/s0036500405932
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 fourthorder elliptic problems are uniformly wellconditioned.


Item type: Article ID code: 4543 Dates: DateEvent31 August 2005Published8 April 2005Published OnlineKeywords: hierarchical bases, splines, c1 finite elements, probability, mathematics, Probabilities. Mathematical statistics, Mathematics, Computational Mathematics, Analysis, Mathematics(all) Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Science > MathematicsDepartment: Faculty of Science > Mathematics and Statistics Depositing user: Strathprints Administrator Date deposited: 01 Nov 2007 Last modified: 19 Jul 2021 01:29 URI: https://strathprints.strath.ac.uk/id/eprint/4543
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