Picture of athlete cycling

Open Access research with a real impact on health...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the Physical Activity for Health Group based within the School of Psychological Sciences & Health. Research here seeks to better understand how and why physical activity improves health, gain a better understanding of the amount, intensity, and type of physical activity needed for health benefits, and evaluate the effect of interventions to promote physical activity.

Explore open research content by Physical Activity for Health...

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

[img]
Preview
Text (strathprints004543)
strathprints004543.pdf - Accepted Author Manuscript

Download (329kB) | Preview

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.