Local lagrange interpolation with cubic C1 splines on tetrahedral partitions

AbstractWe describe an algorithm for constructing a Lagrange interpolation pair based on C1 cubic splines defined on tetrahedral partitions. In particular, given a set of points V∈R3, we construct a set P containing V and a spline space S31(▵) based on a tetrahedral partition ▵ whose set of vertices include V such that interpolation at the points of P is well-defined and unique. Earlier results are extended in two ways: (1) here we allow arbitrary sets V, and (2) the method provides optimal approximation order of smooth functions