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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Official URL: http://dx.doi.org/10.1007/s00365-004-0593-2

## 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.

Item type: | Article |
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ID code: | 4543 |

Keywords: | hierarchical bases, splines, c1 finite elements, probability, mathematics, Probabilities. Mathematical statistics, Mathematics |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

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Depositing user: | Strathprints Administrator |

Date Deposited: | 01 Nov 2007 |

Last modified: | 19 Mar 2012 02:17 |

URI: | http://strathprints.strath.ac.uk/id/eprint/4543 |

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