On the multi-level splitting of finite element spaces
Numerische Mathematik
Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
Hierarchical conforming finite element methods for the biharmonic equation
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
On calculating normalized Powell-Sabin B-splines
Computer Aided Geometric Design
Element-by-Element Construction of Wavelets Satisfying Stability and Moment Conditions
SIAM Journal on Numerical Analysis
Piecewise Quadratic Approximations on Triangles
ACM Transactions on Mathematical Software (TOMS)
Local Lagrange interpolation by bivariate C1 cubic splines
Mathematical Methods for Curves and Surfaces
Macro-elements and stable local bases for splines on Powell-Sabin triangulations
Mathematics of Computation
Automatic construction of control triangles for subdivided Powell-Sabin splines
Computer Aided Geometric Design
On the stability of normalized Powell-Sabin B-splines
Journal of Computational and Applied Mathematics
A second generation wavelet based finite elements on triangulations
Computational Mechanics
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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 under some weak regularity assumptions on the underlying triangulations we prove that they form strongly stable Riesz bases for the Sobolev spaces Hs(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 (Hierarchical Riesz bases for Hs (Ω), 1 s