Recursive computation of bivariate Hermite spline interpolants

Let u be a function defined on a triangulated bounded domain Ω in R2. In this paper, we study a recursive method for the construction of a Hermite spline interpolant uk of class Ck on Ω, defined by some data scheme Dk(u). We show that when Dr−1(u)⊂Dr(u) for all 1⩽r⩽k, the spline function uk can be decomposed as a sum of (k+1) simple elements. As application, we give the decomposition of the Ženišeck polynomial spline of class Ck and degree 4k+1, and we illustrate our results by an example.