{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T02:43:18Z","timestamp":1780972998003,"version":"3.54.1"},"reference-count":20,"publisher":"American Mathematical Society (AMS)","issue":"323","license":[{"start":{"date-parts":[[2021,1,13]],"date-time":"2021-01-13T00:00:00Z","timestamp":1610496000000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1913083"],"award-info":[{"award-number":["1913083"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1719829"],"award-info":[{"award-number":["1719829"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1913083"],"award-info":[{"award-number":["1913083"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1719829"],"award-info":[{"award-number":["1719829"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We construct local exact piecewise polynomial sequences on Alfeld splits in any spatial dimension and any polynomial degree. An Alfeld split of a simplex is obtained by connecting the vertices of an\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n\">\n                        <mml:semantics>\n                          <mml:mi>n<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -simplex with its barycenter. We show that, on these splits, the kernel of the exterior derivative has enhanced smoothness. Byproducts of this result include characterizations of discrete divergence-free subspaces and simple formulas for the dimensions of smooth polynomial spaces. In addition, we construct analogous global exact sequences and commuting projections in three-dimensions with varying levels of smoothness.\n                  <\/p>","DOI":"10.1090\/mcom\/3520","type":"journal-article","created":{"date-parts":[[2020,1,13]],"date-time":"2020-01-13T12:53:02Z","timestamp":1578919982000},"page":"1059-1091","source":"Crossref","is-referenced-by-count":35,"title":["Exact smooth piecewise polynomial sequences on Alfeld splits"],"prefix":"10.1090","volume":"89","author":[{"given":"Guosheng","family":"Fu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johnny","family":"Guzm\u00e1n","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Neilan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2020,1,13]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"P. 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IMACS, 1992."},{"key":"3","isbn-type":"print","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492906210018","article-title":"Finite element exterior calculus, homological techniques, and applications","volume":"15","author":"Arnold, Douglas N.","year":"2006","ISBN":"https:\/\/id.crossref.org\/isbn\/0521868157","journal-title":"Acta Numer.","ISSN":"https:\/\/id.crossref.org\/issn\/0962-4929","issn-type":"print"},{"issue":"4","key":"4","doi-asserted-by":"publisher","first-page":"1461","DOI":"10.1137\/100794250","article-title":"A connection between Scott-Vogelius and grad-div stabilized Taylor-Hood FE approximations of the Navier-Stokes equations","volume":"49","author":"Case, Michael A.","year":"2011","journal-title":"SIAM J. Numer. 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Tocher, Finite Element Stiffness Matrices for Analysis of Plates in Bending, Proceedings of the Conference on Matrix Methods in Structural Mechanics, Wright-Patterson Air Force Base, Ohio, October 1965, 515\u2013545."},{"issue":"2","key":"8","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s00209-009-0517-8","article-title":"On Bogovski\u012d and regularized Poincar\u00e9 integral operators for de Rham complexes on Lipschitz domains","volume":"265","author":"Costabel, Martin","year":"2010","journal-title":"Math. 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