C1 trivariate polynomial interpolation
Computer Aided Geometric Design
A trivariate Powell—Sabin interpolant
Computer Aided Geometric Design
A $C^2$ Trivariate Macroelement Based on the Worsey--Farin Split of a Tetrahedron
SIAM Journal on Numerical Analysis
A C2 trivariate macro-element based on the Clough-Tocher-split of a tetrahedron
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
A C1 quadratic trivariate macro-element space defined over arbitrary tetrahedral partitions
Journal of Approximation Theory
A trivariate clough-tocher scheme for tetrahedral data
Computer Aided Geometric Design
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We propose two tetrahedral C^1 cubic macro elements that are constructed locally on one tetrahedron without any knowledge of the geometry of neighboring tetrahedra. Among such geometrically unconstrained local polynomial tetrahedral C^1 schemes requiring only first order derivative data, our macro elements have the smallest number of coefficients. The resulting macro element spaces are stable and provide full approximation power. We give explicit formulae that can be used to implement our schemes.