Adaptive isogeometric methods with hierarchical splines: Optimality and convergence rates

DOI10.1142/S0218202517500580zbMath1376.41004OpenAlexW2757578344MaRDI QIDQ4595060

Carlotta Giannelli, Annalisa Buffa

Publication date: 28 November 2017

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202517500580

zbMATH Keywords

adaptivityisogeometric analysishierarchical splines

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Spline approximation (41A15)

Related Items (21)

Adaptive isogeometric methods with hierarchical splines: an overview ⋮ Adaptive Isogeometric Phase-Field Modeling of Weak and Strong Discontinuities ⋮ Adaptive BEM for elliptic PDE systems. II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations ⋮ Analysis-aware defeaturing: Problem setting and a posteriori estimation ⋮ Stable implementation of adaptive IGABEM in 2D in MATLAB ⋮ A new perspective on hierarchical spline spaces for adaptivity ⋮ Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach ⋮ Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines ⋮ Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines ⋮ Adaptive isogeometric phase-field modeling of the Cahn-Hilliard equation: suitably graded hierarchical refinement and coarsening on multi-patch geometries ⋮ Adaptive isogeometric boundary element methods with local smoothness control ⋮ Adaptive isogeometric methods with C1 (truncated) hierarchical splines on planar multi-patch domains ⋮ Adaptive IGAFEM with optimal convergence rates: T-splines ⋮ Isogeometric analysis with \(C^1\) hierarchical functions on planar two-patch geometries ⋮ Suitably graded THB-spline refinement and coarsening: towards an adaptive isogeometric analysis of additive manufacturing processes ⋮ Remarks on Poincaré and interpolation estimates for Truncated Hierarchical B-splines ⋮ BPX preconditioners for isogeometric analysis using (truncated) hierarchical B-splines ⋮ Refinement algorithms for adaptive isogeometric methods with hierarchical splines ⋮ A hierarchical approach to the \textit{a posteriori} error estimation of isogeometric Kirchhoff plates and Kirchhoff-Love shells ⋮ Projection and transfer operators in adaptive isogeometric analysis with hierarchical B-splines ⋮ Weighted quadrature for hierarchical B-splines

Uses Software

• ISOGAT

Cites Work

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