{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T13:05:00Z","timestamp":1784898300259,"version":"3.55.0"},"reference-count":33,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T00:00:00Z","timestamp":1782172800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100024370","name":"MIUR","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100024370","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100017142","name":"Francesco Severi National Institute of Higher Mathematics National Group of Scientific Calculations","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100017142","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000900","name":"CIRM","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000900","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Mathematics and Computers in Simulation"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.matcom.2026.06.017","type":"journal-article","created":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T15:08:07Z","timestamp":1781968087000},"page":"1041-1056","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Simplex-splines on the Clough\u2013Tocher split for high-order numerical approximation"],"prefix":"10.1016","volume":"249","author":[{"given":"Jean-Louis","family":"Merrien","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8336-4560","authenticated-orcid":false,"given":"Francesca","family":"Pelosi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0396-5513","authenticated-orcid":false,"given":"Maria Lucia","family":"Sampoli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4110-3308","authenticated-orcid":false,"given":"Hendrik","family":"Speleers","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.matcom.2026.06.017_b1","series-title":"Curves and Surfaces for CAGD: A Practical Guide","author":"Farin","year":"2002"},{"key":"10.1016\/j.matcom.2026.06.017_b2","series-title":"B\u00e9zier and B-Spline Techniques","author":"Prautsch","year":"2002"},{"key":"10.1016\/j.matcom.2026.06.017_b3","series-title":"Isogeometric Analysis: Toward Integration of CAD and FEA","author":"Cottrell","year":"2009"},{"key":"10.1016\/j.matcom.2026.06.017_b4","doi-asserted-by":"crossref","first-page":"4135","DOI":"10.1016\/j.cma.2004.10.008","article-title":"Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement","volume":"194","author":"Hughes","year":"2005","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.matcom.2026.06.017_b5","doi-asserted-by":"crossref","first-page":"1726","DOI":"10.1016\/j.cma.2009.01.021","article-title":"n-Width and sup-infs, and optimality ratios for the k-version of the isogeometric finite element method","volume":"198","author":"Evans","year":"2009","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.matcom.2026.06.017_b6","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1142\/S0218202519500192","article-title":"Sharp error estimates for spline approximation: Explicit constants, n-widths, and eigenfunction convergence","volume":"29","author":"Sande","year":"2019","journal-title":"Math. Models Methods Appl. Sci."},{"key":"10.1016\/j.matcom.2026.06.017_b7","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.cma.2008.07.012","article-title":"Adaptive isogeometric analysis by local h-refinement with T-splines","volume":"199","author":"D\u00f6rfel","year":"2010","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.matcom.2026.06.017_b8","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1145\/882262.882295","article-title":"T-splines and T-NURCCs","volume":"22","author":"Sederberg","year":"2003","journal-title":"ACM Trans. Graph."},{"key":"10.1016\/j.matcom.2026.06.017_b9","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/j.cma.2015.11.002","article-title":"THB-splines: An effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis","volume":"299","author":"Giannelli","year":"2016","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.matcom.2026.06.017_b10","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1016\/j.cagd.2012.03.025","article-title":"THB-splines: The truncated basis for hierarchical splines","volume":"29","author":"Giannelli","year":"2012","journal-title":"Comput. Aided Geom. Design"},{"key":"10.1016\/j.matcom.2026.06.017_b11","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.cagd.2012.12.005","article-title":"Polynomial splines over locally refined box-partitions","volume":"30","author":"Dokken","year":"2013","journal-title":"Comput. Aided Geom. Design"},{"key":"10.1016\/j.matcom.2026.06.017_b12","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/j.cma.2013.09.014","article-title":"Isogeometric analysis using LR B-splines","volume":"269","author":"Johannessen","year":"2014","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.matcom.2026.06.017_b13","series-title":"Spline Functions on Triangulations","author":"Lai","year":"2007"},{"key":"10.1016\/j.matcom.2026.06.017_b14","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2022.114983","article-title":"Generalized C1 Clough\u2013Tocher splines for CAGD and FEM","volume":"395","author":"Gro\u0161elj","year":"2022","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.matcom.2026.06.017_b15","doi-asserted-by":"crossref","DOI":"10.1016\/j.cagd.2023.102194","article-title":"Extraction and application of super-smooth cubic B-splines over triangulations","volume":"103","author":"Gro\u0161elj","year":"2023","journal-title":"Comput. Aided Geom. Design"},{"key":"10.1016\/j.matcom.2026.06.017_b16","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.cad.2013.08.017","article-title":"Isogeometric analysis on triangulations","volume":"46","author":"Jaxon","year":"2014","journal-title":"Comput.-Aided Des."},{"key":"10.1016\/j.matcom.2026.06.017_b17","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.cad.2016.08.002","article-title":"Splines over regular triangulations in numerical simulation","volume":"82","author":"Pelosi","year":"2017","journal-title":"Comput.-Aided Des."},{"key":"10.1016\/j.matcom.2026.06.017_b18","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.cma.2012.02.009","article-title":"Isogeometric analysis with Powell\u2013Sabin splines for advection-diffusion-reaction problems","volume":"221-222","author":"Speleers","year":"2012","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.matcom.2026.06.017_b19","series-title":"Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology","first-page":"45","article-title":"Bernstein\u2013B\u00e9zier form and its role in studying multivariate splines","volume":"vol. 60","author":"Manni","year":"2024"},{"key":"10.1016\/j.matcom.2026.06.017_b20","doi-asserted-by":"crossref","first-page":"1667","DOI":"10.1090\/S0025-5718-2013-02664-6","article-title":"A B-spline-like basis for the Powell\u2013Sabin 12-split based on simplex splines","volume":"82","author":"Cohen","year":"2013","journal-title":"Math. Comp."},{"key":"10.1016\/j.matcom.2026.06.017_b21","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1007\/s10208-022-09553-z","article-title":"Construction of C2 cubic splines on arbitrary triangulations","volume":"22","author":"Lyche","year":"2022","journal-title":"Found. Comput. Math."},{"key":"10.1016\/j.matcom.2026.06.017_b22","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.cagd.2018.07.004","article-title":"Simplex-splines on the Clough\u2013Tocher element","volume":"65","author":"Lyche","year":"2018","journal-title":"Comput. Aided Geom. Design"},{"key":"10.1016\/j.matcom.2026.06.017_b23","doi-asserted-by":"crossref","DOI":"10.1016\/j.cagd.2025.102412","article-title":"A C1 simplex-spline basis for the Alfeld split in Rs","volume":"117","author":"Lyche","year":"2025","journal-title":"Comput. Aided Geom. Design"},{"key":"10.1016\/j.matcom.2026.06.017_b24","first-page":"19","article-title":"Sur l\u2019\u00e9l\u00e9ment de Clough et Tocher","volume":"8","author":"Ciarlet","year":"1974","journal-title":"RAIRO \u2013 Anal. Num\u00e9r."},{"key":"10.1016\/j.matcom.2026.06.017_b25","series-title":"Proceedings of the Conference on Matrix Methods in Structural Mechanics","first-page":"515","article-title":"Finite element stiffness matrices for analysis of plate bending","author":"Clough","year":"1965"},{"key":"10.1016\/j.matcom.2026.06.017_b26","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1051\/m2an\/1979130302271","article-title":"A family of C1 finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems","volume":"13","author":"Douglas","year":"1979","journal-title":"RAIRO \u2013 Anal. Num\u00e9r."},{"key":"10.1016\/j.matcom.2026.06.017_b27","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1016\/j.cagd.2010.09.003","article-title":"A normalized basis for reduced Clough\u2013Tocher splines","volume":"27","author":"Speleers","year":"2010","journal-title":"Comput. Aided Geom. Design"},{"key":"10.1016\/j.matcom.2026.06.017_b28","series-title":"Multivariate Approximation Theory","first-page":"211","article-title":"On a numerically efficient method for computing multivariate B-splines","author":"Micchelli","year":"1979"},{"key":"10.1016\/j.matcom.2026.06.017_b29","series-title":"Approximation Theory XIV","first-page":"283","article-title":"Multivariate C1-continuous splines on the Alfeld split of a simplex","volume":"vol. 83","author":"Kolesnikov","year":"2014"},{"key":"10.1016\/j.matcom.2026.06.017_b30","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/s11075-008-9175-x","article-title":"Computing bivariate splines in scattered data fitting and the finite-element method","volume":"48","author":"Schumaker","year":"2008","journal-title":"Numer. Algorithms"},{"key":"10.1016\/j.matcom.2026.06.017_b31","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2024.117196","article-title":"Quadrature rules for C1 quadratic spline finite elements on the Powell\u2013Sabin 12-split","volume":"430","author":"Eddargani","year":"2024","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.matcom.2026.06.017_b32","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1090\/mcom\/4058","article-title":"Quadrature rules for splines of high smoothness on uniformly refined triangles","volume":"95","author":"Eddargani","year":"2026","journal-title":"Math. Comp."},{"key":"10.1016\/j.matcom.2026.06.017_b33","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1016\/j.cam.2018.10.036","article-title":"Gaussian quadrature for C1 cubic Clough\u2013Tocher macro-triangles","volume":"351","author":"Kosinka","year":"2019","journal-title":"J. Comput. Appl. Math."}],"container-title":["Mathematics and Computers in Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426002600?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426002600?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T12:39:24Z","timestamp":1784896764000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0378475426002600"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":33,"alternative-id":["S0378475426002600"],"URL":"https:\/\/doi.org\/10.1016\/j.matcom.2026.06.017","relation":{},"ISSN":["0378-4754"],"issn-type":[{"value":"0378-4754","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Simplex-splines on the Clough\u2013Tocher split for high-order numerical approximation","name":"articletitle","label":"Article Title"},{"value":"Mathematics and Computers in Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.matcom.2026.06.017","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS).","name":"copyright","label":"Copyright"}]}}