Triangular finite elements of HCT type and class \(C^ \rho\)

DOI10.1007/BF02519038zbMath0832.65003OpenAlexW1965484364MaRDI QIDQ1895903

Paul Sablonniere, Mohammed Laghchim-Lahlou

Publication date: 5 March 1996

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

Full work available at URL: https://doi.org/10.1007/bf02519038

zbMATH Keywords

interpolationpolygonal domainpiecewise polynomial functiontriangular finite elementsHsieh-Clough-Tocher subtriangulation

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical interpolation (65D05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05)

Related Items (15)

Macro-elements and stable local bases for splines on Powell-Sabin triangulations ⋮ Un schéma d'interpolation rationnel sur un quadrilatère de classeC² ⋮ The Nöther and Riemann-Roch type theorems for piecewise algebraic curve ⋮ A new B-spline representation for cubic splines over Powell-Sabin triangulations ⋮ Generalized \(C^1\) Clough-Tocher splines for CAGD and FEM ⋮ Special multivariate quadratic spline space ⋮ A normalized basis for reduced Clough-Tocher splines ⋮ Improving Clough-Tocher interpolants ⋮ \(C^ r\)-finite elements of Powell-Sabin type on the three direction mesh ⋮ Hermite spline interpolation on a three direction mesh from Powell-Sabin and Hsieh-Clough-Tocher finite elements ⋮ Fitting scattered data on sphere-like surfaces using spherical splines ⋮ \(C^r\) rational splines over a triangulation ⋮ Interpolation by spline spaces on classes of triangulations ⋮ Simplex-splines on the Clough-Tocher split with arbitrary smoothness ⋮ Developments in bivarite spline interpolation

Cites Work

• Multivariate vertex splines and finite elements
• A modified Clough-Tocher interpolant
• Composite finite elements of class \(C^ k\)
• A bivariate \(C^ 2\) Clough-Tocher scheme
• Super spline spaces of smoothness \(r\) and degree \(d\geq{} 3r+2\)
• On the dimension of bivariate spline spaces of smoothness r and degree \(d=3r+1\)
• General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods
• On Cubic and Quartic Clough–Tocher Finite Elements
• Interpolation Error Estimates for the Reduced Hsieh-Clough-Tocher Triangle
• On Super Splines and Finite Elements
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