Construction of local 𝐶¹ quartic spline elements for optimal-order approximation

DOI10.1090/S0025-5718-96-00689-8zbMath0854.41020OpenAlexW2029355303MaRDI QIDQ4878532

Dong Hong, Charles K. Chui

Publication date: 27 January 1997

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-96-00689-8

zbMATH Keywords

order of approximationsplines on arbitrary triangulationClough-Tocher triangle

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Multidimensional problems (41A63) Interpolation in approximation theory (41A05) Rate of convergence, degree of approximation (41A25) Spline approximation (41A15)

Related Items

Optimal Lagrange interpolation by quartic \(C^1\) splines on triangulations ⋮ Interpolation by \(C^1\) splines of degree \(q\geq 4\) on triangulations ⋮ New approach to study splines by blossoming method and application to the construction of a bivariate \(C^1\) quartic quasi-interpolant ⋮ An explicit quasi-interpolation scheme based on \(C^1\) quartic splines on type-1 triangulations ⋮ An explicit local basis for \(C^{1}\) cubic spline spaces over a triangulated quadrangulation ⋮ Some new formulations of smoothness conditions and conformality conditions for bivariate splines ⋮ Optimal-order approximation by mixed three-directional spline elements ⋮ Interpolation by spline spaces on classes of triangulations ⋮ Developments in bivarite spline interpolation

Cites Work

• A sharp upper bound on the approximation order of smooth bivariate pp functions
• An Explicit Basis for $C^1 $ Quartic Bivariate Splines
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