O. Davydov and R. Stevenson, Hierarchical Riesz Bases for H^s(\Omega), 1 < s < 5/2, Constr. Approx. 43 (2005), 365-394. DOI 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 ([5]), 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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