{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:35:31Z","timestamp":1777379731514,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T00:00:00Z","timestamp":1698019200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Spanish MINECO project","award":["PID2020-117211GB-I00"],"award-info":[{"award-number":["PID2020-117211GB-I00"]}]},{"name":"Spanish MINECO project","award":["CIAICO\/2021\/227"],"award-info":[{"award-number":["CIAICO\/2021\/227"]}]},{"name":"GVA project","award":["PID2020-117211GB-I00"],"award-info":[{"award-number":["PID2020-117211GB-I00"]}]},{"name":"GVA project","award":["CIAICO\/2021\/227"],"award-info":[{"award-number":["CIAICO\/2021\/227"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The aim of this paper is to present and study nonlinear bivariate C1 quadratic spline quasi-interpolants on uniform criss-cross triangulations for the approximation of piecewise smooth functions. Indeed, by using classical spline quasi-interpolants, the Gibbs phenomenon appears when approximating near discontinuities. Here, we use weighted essentially non-oscillatory techniques to modify classical quasi-interpolants in order to avoid oscillations near discontinuities and maintain high-order accuracy in smooth regions. We study the convergence properties of the proposed quasi-interpolants and we provide some numerical and graphical tests confirming the theoretical results.<\/jats:p>","DOI":"10.3390\/axioms12101002","type":"journal-article","created":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T10:32:24Z","timestamp":1698057144000},"page":"1002","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Nonlinear 2D C1 Quadratic Spline Quasi-Interpolants on Triangulations for the Approximation of Piecewise Smooth Functions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9228-4159","authenticated-orcid":false,"given":"Francesc","family":"Ar\u00e0ndiga","sequence":"first","affiliation":[{"name":"Departament of Mathematics, Universitat de Val\u00e8ncia, Av. Vicent Andr\u00e9s Estell\u00e9s, E-46100 Burjassot, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4259-1657","authenticated-orcid":false,"given":"Sara","family":"Remogna","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Torino, Via Carlo Alberto 10, 10123 Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Buhmann, M., and J\u00e4ger, J. (2022). Quasi-Interpolation, Cambridge University Press.","DOI":"10.1017\/9781139680523"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1687","DOI":"10.1002\/mma.8602","article-title":"Spline quasi-interpolation in the Bernstein basis and its application to digital elevation models","volume":"46","author":"Barrera","year":"2023","journal-title":"Math. Methods Appl. 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