Optimal spline spaces of higher degree for \(L^2\) \(n\)-widths

DOI10.1016/j.jat.2016.12.002zbMath1358.41007OpenAlexW2560948221MaRDI QIDQ514214

Espen Sande, Michael S. Floater

Publication date: 28 February 2017

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2016.12.002

zbMATH Keywords

splinesGreen's functionstotal positivityisogeometric analysis\(n\)-widths

Mathematics Subject Classification ID

Integral operators (47G10) Spline approximation (41A15) Best constants in approximation theory (41A44)

Related Items

Discretization error estimates for discontinuous Galerkin isogeometric analysis, Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems, On periodic \(L^2 n\)-widths, Robust approximation error estimates and multigrid solvers for isogeometric multi-patch discretizations, Removal of spurious outlier frequencies and modes from isogeometric discretizations of second- and fourth-order problems in one, two, and three dimensions, Some remarks on spectral convergence and stability of iso-geometric analysis, Fast multigrid solvers for conforming and non-conforming multi-patch isogeometric analysis, Sharp error estimates for spline approximation: Explicit constants, n-widths, and eigenfunction convergence, Explicit error estimates for spline approximation of arbitrary smoothness in isogeometric analysis, Optimal spline spaces for \(L^2\ n\)-width problems with boundary conditions, Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations, Approximation in FEM, DG and IGA: a theoretical comparison, Best Low-rank Approximations and Kolmogorov $n$-widths

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(n\)-widths, sup-infs, and optimality ratios for the \(k\)-version of the isogeometric finite element method
• Spline spaces are optimal for \(L^2\) n-width
• On principles for the selection of shape functions for the generalized finite element method
• Approximation error estimates and inverse inequalities for B-splines of maximum smoothness
• On n-Widths in L ∞
• DUALITY OF CONVEX FUNCTIONS AND EXTREMUM PROBLEMS