The structure of multivariate superspline spaces of high degree

Alfeld, Peter; Sirvent, Maritza

doi:10.1090/S0025-5718-1991-1079007-2

The structure of multivariate superspline spaces of high degree
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by Peter Alfeld and Maritza Sirvent PDF

Math. Comp. 57 (1991), 299-308 Request permission

Abstract:

We consider splines (of global smoothness r, polynomial degree d, in a general number k of independent variables, defined on a k-dimensional triangulation $\mathcal {T}$ of a suitable domain $\Omega$) which are $r{2^{k - m - 1}}$-times differentiable across every m-face $(m = 0, \cdots ,k - 1)$ of a simplex in $\mathcal {T}$. For the case $d > r{2^k}$ we identify a structure that allows the construction of a minimally supported basis.

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