Approximation of patches by CrCr-finite elements of Powell–Sabin type

In this work we develop a method to extend a function that is defined in a finite set of disjoint patches to a bigger domain containing all of them. The way to extend the function is by minimizing an energy functional which controls the closeness of the extended function to the original one over the patches, as well as the smoothness of the final reconstructed function. We show the existence and uniqueness of solution of this problem and we give a convergence result as well as several graphical and numerical examples.