Recursive computation of bivariate Hermite spline interpolants Original Research Article

Let u be a function defined on a triangulated bounded domain Ω in R2R2. In this paper, we study a recursive method for the construction of a Hermite spline interpolant ukuk of class CkCk on Ω, defined by some data scheme Dk(u)Dk(u). We show that when Dr−1(u)⊂Dr(u)Dr−1(u)⊂Dr(u) for all 1⩽r⩽k1⩽r⩽k, the spline function ukuk can be decomposed as a sum of (k+1)(k+1) simple elements. As application, we give the decomposition of the Ženišeck polynomial spline of class CkCk and degree 4k+14k+1, and we illustrate our results by an example.