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

Oleg Davydov; Rob Stevenson

doi:10.1007/s00365-004-0593-2

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

Oleg Davydov, Rob Stevenson

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	365-394
Number of pages	30
Journal	Constructive Approximation
Volume	22
Issue number	3
Early online date	8 Apr 2005
DOIs	https://doi.org/10.1007/s00365-004-0593-2
Publication status	Published - 31 Aug 2005

Keywords

hierarchical bases
splines
c1 finite elements
probability
mathematics

Access to Document

10.1007/s00365-004-0593-2

strathprints004543Accepted author manuscript, 321 KB

Fingerprint Dive into the research topics of 'Hierarchical Riesz bases for Hs(Omega), 1 < s < 5/2'. Together they form a unique fingerprint.

Cite this

@article{2fca8ed27e844455b4ced34a721c778b,

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

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.",

keywords = "hierarchical bases, splines, c1 finite elements, probability, mathematics",

author = "Oleg Davydov and Rob Stevenson",

year = "2005",

month = aug,

day = "31",

doi = "10.1007/s00365-004-0593-2",

language = "English",

volume = "22",

pages = "365--394",

journal = "Constructive Approximation",

issn = "0176-4276",

number = "3",

}

TY - JOUR

T1 - Hierarchical Riesz bases for Hs(Omega), 1 < s < 5/2

AU - Davydov, Oleg

AU - Stevenson, Rob

PY - 2005/8/31

Y1 - 2005/8/31

N2 - 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.

AB - 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.

KW - hierarchical bases

KW - splines

KW - c1 finite elements

KW - probability

KW - mathematics

U2 - 10.1007/s00365-004-0593-2

DO - 10.1007/s00365-004-0593-2

M3 - Article

VL - 22

SP - 365

EP - 394

JO - Constructive Approximation

JF - Constructive Approximation

SN - 0176-4276

IS - 3

ER -