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

Oleg Davydov, Rob Stevenson

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
13 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)365-394
Number of pages30
JournalConstructive Approximation
Volume22
Issue number3
Early online date8 Apr 2005
DOIs
Publication statusPublished - 31 Aug 2005

Keywords

  • hierarchical bases
  • splines
  • c1 finite elements
  • probability
  • mathematics

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