{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T23:51:42Z","timestamp":1785541902516,"version":"3.56.0"},"reference-count":21,"publisher":"American Mathematical Society (AMS)","issue":"316","license":[{"start":{"date-parts":[[2019,4,16]],"date-time":"2019-04-16T00:00:00Z","timestamp":1555372800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["1620100"],"award-info":[{"award-number":["1620100"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We prove that the Scott-Vogelius finite elements are inf-sup stable on shape-regular meshes for piecewise quartic velocity fields and higher (\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k greater-than-or-equal-to 4\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>\n                              \u2265\n                              \n                            <\/mml:mo>\n                            <mml:mn>4<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k \\ge 4<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ).\n                  <\/p>","DOI":"10.1090\/mcom\/3346","type":"journal-article","created":{"date-parts":[[2017,12,13]],"date-time":"2017-12-13T09:22:01Z","timestamp":1513156921000},"page":"515-529","source":"Crossref","is-referenced-by-count":59,"title":["The Scott-Vogelius finite elements revisited"],"prefix":"10.1090","volume":"88","author":[{"given":"Johnny","family":"Guzm\u00e1n","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L.","family":"Scott","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2018,4,16]]},"reference":[{"key":"1","unstructured":"D. N. Arnold and J. Qin, Quadratic velocity\/linear pressure stokes elements, Advances in Computer Methods for Partial Differential Equations 7 (1992), 28\u201334."},{"issue":"169","key":"2","doi-asserted-by":"publisher","first-page":"71","DOI":"10.2307\/2007793","article-title":"Analysis of some finite elements for the Stokes problem","volume":"44","author":"Bernardi, Christine","year":"1985","journal-title":"Math. 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Hu, Generalized finite element systems for smooth differential forms and Stokes problem, ArXiv e-prints (2016)."},{"issue":"3","key":"11","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1137\/15M1047696","article-title":"On the divergence constraint in mixed finite element methods for incompressible flows","volume":"59","author":"John, Volker","year":"2017","journal-title":"SIAM Rev.","ISSN":"https:\/\/id.crossref.org\/issn\/1095-7200","issn-type":"print"},{"issue":"41-44","key":"12","doi-asserted-by":"publisher","first-page":"3278","DOI":"10.1016\/j.cma.2009.06.016","article-title":"Collision in a cross-shaped domain\u2014a steady 2d Navier-Stokes example demonstrating the importance of mass conservation in CFD","volume":"198","author":"Linke, Alexander","year":"2009","journal-title":"Comput. Methods Appl. Mech. Engrg.","ISSN":"https:\/\/id.crossref.org\/issn\/0045-7825","issn-type":"print"},{"issue":"2","key":"13","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1051\/m2an\/2016032","article-title":"Divergence free virtual elements for the Stokes problem on polygonal meshes","volume":"51","author":"Beir\u00e3o da Veiga, Lourenco","year":"2017","journal-title":"ESAIM Math. Model. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/2822-7840","issn-type":"print"},{"issue":"295","key":"14","doi-asserted-by":"publisher","first-page":"2059","DOI":"10.1090\/S0025-5718-2015-02958-5","article-title":"Discrete and conforming smooth de Rham complexes in three dimensions","volume":"84","author":"Neilan, Michael","year":"2015","journal-title":"Math. 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Zhang, On the family of divergence-free finite elements on tetrahedral grids for the stokes equations, Preprint University of Delaware (2007)."},{"issue":"274","key":"21","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1090\/S0025-5718-2010-02412-3","article-title":"Divergence-free finite elements on tetrahedral grids for \ud835\udc58\u22656","volume":"80","author":"Zhang, Shangyou","year":"2011","journal-title":"Math. 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