**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.

**Preprint version available:**
pdf

Homepage