Equivalence between C1 -continuous Cubic B-splines and Cubic Hermite Polynomials in Finite Element and Collocation Methods

In this paper, we will show that the C 1 -continuous B-spline functional set of polynomial degree p = 3 , can be written as a linear transformation of the well-known piecewise cubic Hermite polynomials. This change of functional basis means that the global B-spline finite element solution is equivalent to that of usual piecewise finite elements in conjunction with cubic Hermite polynomials, with two degrees per nodal point, like those used in beam-bending analysis. In this context, we validate the equivalence between the global Bspline solution and the piecewise solution in boundary-value and eigenvalue problems, for collocation and RitzGalerkin methods.