\(C^{1}\) hierarchical Riesz bases of Lagrange type on Powell-Sabin triangulations

DOI10.1016/j.cam.2005.08.010zbMath1097.65037OpenAlexW2073763435MaRDI QIDQ2499790

Adhemar Bultheel, Jan Maes

Publication date: 14 August 2006

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.08.010

zbMATH Keywords

splinespreconditioninghierarchical basesfourth-order elliptic equationsPowell-Sabin triangulations\(C^{1}\) finite elements

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (4)

A Hermite interpolatory subdivision scheme for \(C^2\)-quintics on the Powell-Sabin 12-split ⋮ A second generation wavelet based finite elements on triangulations ⋮ \(C^1\) piecewise quadratic hierarchical bases ⋮ \(C^1\) triangular isogeometric analysis of the von Karman equations

Cites Work

• On the stability of normalized Powell--Sabin B-splines
• Hierarchical Riesz bases for \(H^{s}(\Omega),\;1 < s < \frac{5}{2}\)
• Stable multiresolution analysis on triangles for surface compression
• On the multi-level splitting of finite element spaces
• On the approximation power of bivariate splines
• \(C^ 1\)-hierarchical bases
• On calculating normalized Powell-Sabin B-splines
• Locally supported, piecewise polynomial biorthogonal wavelets on nonuniform meshes
• Local decomposition of refinable spaces and wavelets
• Automatic construction of control triangles for subdivided Powell --- Sabin splines
• Bounds for a class of linear functionals with applications to Hermite interpolation
• Hierarchical Conforming Finite Element Methods for the Biharmonic Equation
• Piecewise Quadratic Approximations on Triangles
• Macro-elements and stable local bases for splines on Powell-Sabin triangulations
• Element-by-Element Construction of Wavelets Satisfying Stability and Moment Conditions
• Wavelets on Manifolds I: Construction and Domain Decomposition
• SURFACE COMPRESSION WITH HIERARCHICAL POWELL–SABIN B-SPLINES
• Equivalent Norms for Sobolev Spaces
• POWELL–SABIN SPLINE WAVELETS

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