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 |
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Pages (from-to) | 365-394 |
Number of pages | 30 |
Journal | Constructive Approximation |
Volume | 22 |
Issue number | 3 |
Early online date | 8 Apr 2005 |
DOIs | |
Publication status | Published - 31 Aug 2005 |
Keywords
- hierarchical bases
- splines
- c1 finite elements
- probability
- mathematics