Hierarchical spline spaces: quasi-interpolants and local approximation estimates

DOI10.1007/s10444-016-9483-yzbMath1370.41021OpenAlexW2534076154MaRDI QIDQ2400479

Hendrik Speleers

Publication date: 1 September 2017

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-016-9483-y

zbMATH Keywords

hierarchical basesquasi-interpolationlocal refinementlocal approximationtensor-product B-splines

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Spline approximation (41A15) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (19)

Adaptive scattered data fitting by extension of local approximations to hierarchical splines ⋮ Adaptive fitting with THB-splines: error analysis and industrial applications ⋮ Weighted isogeometric collocation based on spline projectors ⋮ Local (T)HB-spline projectors via restricted hierarchical spline fitting ⋮ A new B-spline type approximation method for non-smooth functions ⋮ Efficient matrix assembly in isogeometric analysis with hierarchical B-splines ⋮ Adaptive refinement with locally linearly independent LR B-splines: theory and applications ⋮ Modified PHT-splines ⋮ Local approximation from spline spaces on box meshes ⋮ A posteriori error estimators for hierarchical B-spline discretizations ⋮ Efficient matrix computation for isogeometric discretizations with hierarchical B-splines in any dimension ⋮ Modified basis functions for MPHT-splines ⋮ Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes ⋮ Improved conditioning of isogeometric analysis matrices for trimmed geometries ⋮ Quasi-interpolation for analysis-suitable T-splines ⋮ On spline quasi-interpolation through dimensions ⋮ DPB-splines: the decoupled basis of patchwork splines ⋮ THB-spline approximations for turbine blade design with local B-spline approximations ⋮ Explicit multivariate approximations from cell-average data

Uses Software

• ISOGAT

Cites Work

• A hierarchical approach to adaptive local refinement in isogeometric analysis
• THB-splines: The truncated basis for hierarchical splines
• Strongly stable bases for adaptively refined multilevel spline spaces
• Quasi-hierarchical Powell-Sabin B-splines
• Bivariate hierarchical Hermite spline quasi-interpolation
• Effortless quasi-interpolation in hierarchical spaces
• Local spline approximation methods
• On Bernstein and Markov-type inequalities for multivariate polynomials on convex bodies
• Locally tensor product functions
• Spline approximation by quasiinterpolants
• On Bernstein-Markov-type inequalities for multivariate polynomials in \(L_q\)-norm
• Adaptive isogeometric methods with hierarchical splines: Error estimator and convergence
• Data Dependent Triangulations for Piecewise Linear Interpolation
• Central factorial numbers; their main properties and some applications.
• On the Local Approximation Power of Quasi-Hierarchical Powell-Sabin Splines
• A practical guide to splines.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Hierarchical spline spaces: quasi-interpolants and local approximation estimates