A new approach to deal with C2 cubic splines and its application to super-convergent quasi-interpolation

In this paper, we construct a novel normalized B-spline-like representation for C-2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative functions that are geometrically constructed and form a convex partition of unity. With the help of the control polynomial theory introduced herein, a Marsden identity is derived, from which several families of super-convergent quasi-interpolation operators are defined. (C) 2021 The Author(s). Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS).

Automated summary

In this paper, a novel normalized B-spline-like representation is constructed for a C-2-continuous cubic spline space defined on a refined initial partition. The basis functions are compactly supported non-negative functions that are geometrically constructed and form a convex partition of unity. Through the introduction of control polynomial theory, a Marsden identity is derived, and several families of super-convergent quasi-interpolation operators are defined.