C¹ hierarchical Riesz bases of Lagrange type on Powell-Sabin triangulations

In this paper we construct C¹ continuous piecewise quadratic hierarchical bases on Powell-Sabin triangulations of arbitrary polygonal domains in ℝ². Our bases are of Lagrange type instead of the usual Hermite type and we prove that they form strongly stable Riesz bases for the Sobolev spaces H^s(Ω) with s ∈ (1, 5/2). Especially the case s = 2 is of interest, because we can use the corresponding hierarchical basis for preconditioning fourth order elliptic equations leading to uniformly well-conditioned stiffness matrices. Compared to the hierarchical Riesz bases by Davydov and Stevenson our construction is simpler.nrpages: 15status: publishe