Hierarchical Riesz Bases for Hs(Ω), 1 < s < 5/2 |
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Authors: | Oleg Davydov Rob Stevenson |
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Institution: | (1) Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, Scotland;(2) Department of Mathematics, Utrecht University, P.O. Box 80.010, 3508 TA Utrecht , The Netherlands |
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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. |
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Keywords: | Hierarchical bases Splines C1 Finite elements |
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