Energy minimization method for scattered data Hermite interpolation

Given a set of scattered data with derivatives values, we use a minimal energy method to find Hermite interpolation based on bivariate spline spaces over a triangulation of the scattered data locations. We show that the minimal energy method produces a unique Hermite spline interpolation of the given scattered data with derivative values. Also we show that the Hermite spline interpolation converges to a given sufficiently smooth function f if the data values are obtained from this f. That is, the surface of the Hermite spline interpolation resembles the given set of derivative values. Some numerical examples are presented to demonstrate our method.