A new approach to deal with C2 cubic splines and its application to super-convergent quasi-interpolation Barrera Rosillo, Domingo Eddargani, Salah Ibáñez Pérez, María José Bernstein-Bézier representation Hermite interpolation Normalized B-splines Super-convergent quasi-interpolants Control polynomials The authors wish to thank the anonymous referees for their very pertinent and useful comments which helped them to improve the original manuscript. The first and third authors are members of the research group FQM 191 Matematica Aplicada funded by the PAIDI programme of the Junta de Andalucia, Spain. The second author would like to thank the University of Granada, Spain for the financial support for the research stay during which this work was carried out. Funding for open access charge: Universidad de Granada/CBUA In this paper, we construct a novel normalized B-spline-like representation for C2-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. 2022-05-31T07:04:10Z 2022-05-31T07:04:10Z 2021-12-13 info:eu-repo/semantics/article D. Barrera... [et al.]. A new approach to deal with C2 cubic splines and its application to super-convergent quasi-interpolation, Mathematics and Computers in Simulation, Volume 194, 2022, Pages 401-415, ISSN 0378-4754, [https://doi.org/10.1016/j.matcom.2021.12.003] http://hdl.handle.net/10481/75119 10.1016/j.matcom.2021.12.003 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España Elsevier