Quasi-interpolation by C1 quartic splines on type-1 triangulations Barrera Rosillo, Domingo Dagnino, Catterina Ibáñez Pérez, María José Remogna, Sara This work was initiated during the visiting on 2017, March of the first and third authors to the Department of Mathematics of the University of Torino, and partially realized during the visiting of the fourth author to the Department of Applied Mathematics of the University of Granada on 2017, November. They thank the financial support of both institutions and the Gruppo Nazionale per il Calcolo Scientifico (GNCS) - INdAM. In this paper we construct two new families of C1 quartic quasi-interpolating splines on type-1 triangulations approximating regularly distributed data. The splines are directly determined by setting their Bernstein–Bézier coefficients to appropriate combinations of the given data values instead of defining the approximating splines as linear combinations of compactly supported bivariate spanning functions and do not use prescribed derivatives at any point of the domain. The quasi-interpolation operators provided by the proposed schemes interpolate the data values at the vertices of the triangulation, reproduce cubic polynomials and yield approximation order four for smooth functions. We also propose some numerical tests that confirm the theoretical results. 2024-01-30T11:08:42Z 2024-01-30T11:08:42Z 2019-03-15 journal article D. Barrera, C. Dagnino, M.J. Ibáñez, S. Remogna, Quasi-interpolation by C1 quartic splines on type-1 triangulations, Journal of Computational and Applied Mathematics, 349 (2019) 225-238, https://doi.org/10.1016/j.cam.2018.08.005 https://hdl.handle.net/10481/87622 10.1016/j.cam.2018.08.005 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ open access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Elsevier B.V.