{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T06:39:01Z","timestamp":1775716741127,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,7,3]],"date-time":"2022-07-03T00:00:00Z","timestamp":1656806400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,7,3]],"date-time":"2022-07-03T00:00:00Z","timestamp":1656806400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-05606-2015"],"award-info":[{"award-number":["RGPIN-05606-2015"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2022,8]]},"DOI":"10.1007\/s10915-022-01889-6","type":"journal-article","created":{"date-parts":[[2022,7,3]],"date-time":"2022-07-03T12:02:10Z","timestamp":1656849730000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Analysis of Pressure-Robust Embedded-Hybridized Discontinuous Galerkin Methods for the Stokes Problem Under Minimal Regularity"],"prefix":"10.1007","volume":"92","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0542-4342","authenticated-orcid":false,"given":"Aaron","family":"Baier-Reinio","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6036-0356","authenticated-orcid":false,"given":"Sander","family":"Rhebergen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5291-7951","authenticated-orcid":false,"given":"Garth N.","family":"Wells","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,7,3]]},"reference":[{"issue":"4","key":"1889_CR1","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/BF02576171","volume":"21","author":"DN Arnold","year":"1984","unstructured":"Arnold, D.N., Brezzi, F., Fortin, M.: A stable finite element for the Stokes equations. Calcolo 21(4), 337\u2013344 (1984). https:\/\/doi.org\/10.1007\/BF02576171","journal-title":"Calcolo"},{"issue":"2","key":"1889_CR2","doi-asserted-by":"publisher","first-page":"800","DOI":"10.1093\/imanum\/drt022","volume":"34","author":"S Badia","year":"2013","unstructured":"Badia, S., Codina, R., Gudi, T., Guzm\u00e1n, J.: Error analysis of discontinuous Galerkin methods for the Stokes problem under minimal regularity. IMA J. Numer. Anal. 34(2), 800\u2013819 (2013). https:\/\/doi.org\/10.1093\/imanum\/drt022","journal-title":"IMA J. Numer. Anal."},{"issue":"169","key":"1889_CR3","doi-asserted-by":"publisher","first-page":"71","DOI":"10.2307\/2007793","volume":"44","author":"C Bernardi","year":"1985","unstructured":"Bernardi, C., Raugel, G.: Analysis of some finite elements for the Stokes problem. Math. Comput. 44(169), 71\u201379 (1985). https:\/\/doi.org\/10.2307\/2007793","journal-title":"Math. Comput."},{"key":"1889_CR4","doi-asserted-by":"publisher","unstructured":"Boffi, D., Brezzi, F., Fortin, M.: Mixed Finite Element Methods and Applications, Springer Series in Computational Mathematics, vol.\u00a044. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-36519-5","DOI":"10.1007\/978-3-642-36519-5"},{"key":"1889_CR5","doi-asserted-by":"publisher","unstructured":"Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods, Texts in Applied Mathematics, vol.\u00a015, 3rd edn. Springer, New York (2008). https:\/\/doi.org\/10.1007\/978-0-387-75934-0","DOI":"10.1007\/978-0-387-75934-0"},{"key":"1889_CR6","doi-asserted-by":"publisher","unstructured":"Chorfi, N.: Geometric singularities of the Stokes problem. Abstr. Appl. Anal. 2014, Article ID 491326 (2014). https:\/\/doi.org\/10.1155\/2014\/491326","DOI":"10.1155\/2014\/491326"},{"issue":"2","key":"1889_CR7","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1137\/070706616","volume":"47","author":"B Cockburn","year":"2009","unstructured":"Cockburn, B., Gopalakrishnan, J., Lazarov, R.: Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. SIAM J. Numer. Anal. 47(2), 1319\u20131365 (2009). https:\/\/doi.org\/10.1137\/070706616","journal-title":"SIAM J. Numer. Anal."},{"issue":"1\u20132","key":"1889_CR8","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/s10915-006-9107-7","volume":"31","author":"B Cockburn","year":"2007","unstructured":"Cockburn, B., Kanschat, G., Sch\u00f6tzau, D.: A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations. J. Sci. Comput. 31(1\u20132), 61\u201373 (2007). https:\/\/doi.org\/10.1007\/s10915-006-9107-7","journal-title":"J. Sci. Comput."},{"issue":"288","key":"1889_CR9","doi-asserted-by":"publisher","first-page":"1571","DOI":"10.1090\/S0025-5718-2014-02802-0","volume":"83","author":"B Cockburn","year":"2014","unstructured":"Cockburn, B., Sayas, F.-J.: Divergence-conforming HDG methods for Stokes flows. Math. Comput. 83(288), 1571\u20131598 (2014). https:\/\/doi.org\/10.1090\/S0025-5718-2014-02802-0","journal-title":"Math. Comput."},{"key":"1889_CR10","doi-asserted-by":"crossref","unstructured":"Dauge, M.: Elliptic Boundary Value Problems on Corner Domains. Lecture Notes in Mathematics, vol. 1341. Springer, Berlin (1988)","DOI":"10.1007\/BFb0086682"},{"issue":"1","key":"1889_CR11","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1137\/0520006","volume":"20","author":"M Dauge","year":"1989","unstructured":"Dauge, M.: Stationary Stokes and Navier-Stokes systems on two- or three-dimensional domains with corners. Part I. Linearized equations. SIAM J. Math. Anal. 20(1), 74\u201397 (1989). https:\/\/doi.org\/10.1137\/0520006","journal-title":"SIAM J. Math. Anal."},{"key":"1889_CR12","doi-asserted-by":"publisher","unstructured":"Di Pietro, D.A., Ern, A.: Mathematical Aspects of Discontinuous Galerkin Methods, Math\u00e9matiques et Applications, vol.\u00a069. Springer, Berlin (2012). https:\/\/doi.org\/10.1007\/978-3-642-22980-0","DOI":"10.1007\/978-3-642-22980-0"},{"issue":"150","key":"1889_CR13","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1090\/S0025-5718-1980-0559195-7","volume":"34","author":"T Dupont","year":"1980","unstructured":"Dupont, T., Scott, R.: Polynomial approximation of functions in Sobolev spaces. Math. Comput. 34(150), 441\u2013463 (1980). https:\/\/doi.org\/10.1090\/S0025-5718-1980-0559195-7","journal-title":"Math. Comput."},{"key":"1889_CR14","doi-asserted-by":"publisher","unstructured":"Ern, A., Guermond, J.-L.: Theory and Practice of Finite Elements, Applied Mathematical Sciences, vol. 159. Springer, New York (2004). https:\/\/doi.org\/10.1007\/978-1-4757-4355-5","DOI":"10.1007\/978-1-4757-4355-5"},{"issue":"4","key":"1889_CR15","doi-asserted-by":"publisher","first-page":"1367","DOI":"10.1051\/m2an\/2016066","volume":"51","author":"A Ern","year":"2017","unstructured":"Ern, A., Guermond, J.-L.: Finite element quasi-interpolation and best approximation. ESAIM Math. Model. Numer. Anal. 51(4), 1367\u20131385 (2017). https:\/\/doi.org\/10.1051\/m2an\/2016066","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"1889_CR16","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1016\/j.cma.2018.11.012","volume":"345","author":"G Fu","year":"2019","unstructured":"Fu, G.: An explicit divergence-free DG method for incompressible flow. Comput. Methods Appl. Mech. Eng. 345, 502\u2013517 (2019). https:\/\/doi.org\/10.1016\/j.cma.2018.11.012","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"7","key":"1889_CR17","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1002\/nme.1893","volume":"70","author":"S G\u00fczey","year":"2007","unstructured":"G\u00fczey, S., Cockburn, B., Stolarski, H.K.: The embedded discontinuous Galerkin method: application to linear shell problems. Int. J. Numer. Methods Eng. 70(7), 757\u2013790 (2007). https:\/\/doi.org\/10.1002\/nme.1893","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"285","key":"1889_CR18","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1090\/S0025-5718-2013-02753-6","volume":"83","author":"J Guzm\u00e1n","year":"2014","unstructured":"Guzm\u00e1n, J., Neilan, M.: Conforming and divergence-free Stokes elements on general triangular meshes. Math. Comput. 83(285), 15\u201336 (2014). https:\/\/doi.org\/10.1090\/S0025-5718-2013-02753-6","journal-title":"Math. Comput."},{"issue":"4","key":"1889_CR19","doi-asserted-by":"publisher","first-page":"1489","DOI":"10.1093\/imanum\/drt053","volume":"34","author":"J Guzm\u00e1n","year":"2014","unstructured":"Guzm\u00e1n, J., Neilan, M.: Conforming and divergence-free Stokes elements in three dimensions. IMA J. Numer. Anal. 34(4), 1489\u20131508 (2014). https:\/\/doi.org\/10.1093\/imanum\/drt053","journal-title":"IMA J. Numer. Anal."},{"issue":"3","key":"1889_CR20","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1137\/15M1047696","volume":"59","author":"V John","year":"2017","unstructured":"John, V., Linke, A., Merdon, C., Neilan, M., Rebholz, L.G.: On the divergence constraint in mixed finite element methods for incompressible flows. SIAM Rev. 59(3), 492\u2013544 (2017). https:\/\/doi.org\/10.1137\/15M1047696","journal-title":"SIAM Rev."},{"issue":"6","key":"1889_CR21","doi-asserted-by":"publisher","first-page":"2374","DOI":"10.1137\/S0036142902405217","volume":"41","author":"OA Karakashian","year":"2003","unstructured":"Karakashian, O.A., Pascal, F.: A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems. SIAM J. Numer. Anal. 41(6), 2374\u20132399 (2003). https:\/\/doi.org\/10.1137\/S0036142902405217","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"1889_CR22","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1016\/0022-1236(76)90035-5","volume":"21","author":"RB Kellogg","year":"1976","unstructured":"Kellogg, R.B., Osborn, J.E.: A regularity result for the Stokes problem in a convex polygon. J. Funct. Anal. 21(4), 397\u2013431 (1976). https:\/\/doi.org\/10.1016\/0022-1236(76)90035-5","journal-title":"J. Funct. Anal."},{"issue":"2","key":"1889_CR23","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1515\/cmam-2020-0023","volume":"21","author":"C Kreuzer","year":"2021","unstructured":"Kreuzer, C., Verf\u00fcrth, R., Zanotti, P.: Quasi-optimal and pressure robust discretizations of the Stokes equations by moment- and divergence-preserving operators. Comput. Methods Appl. Math. 21(2), 423\u2013443 (2021). https:\/\/doi.org\/10.1515\/cmam-2020-0023","journal-title":"Comput. Methods Appl. Math."},{"issue":"4","key":"1889_CR24","doi-asserted-by":"publisher","first-page":"2553","DOI":"10.1093\/imanum\/drz044","volume":"40","author":"C Kreuzer","year":"2019","unstructured":"Kreuzer, C., Zanotti, P.: Quasi-optimal and pressure-robust discretizations of the Stokes equations by new augmented Lagrangian formulations. IMA J. Numer. Anal. 40(4), 2553\u20132583 (2019). https:\/\/doi.org\/10.1093\/imanum\/drz044","journal-title":"IMA J. Numer. Anal."},{"issue":"2","key":"1889_CR25","doi-asserted-by":"publisher","first-page":"A889","DOI":"10.1137\/100818583","volume":"34","author":"RJ Labeur","year":"2012","unstructured":"Labeur, R.J., Wells, G.N.: Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations. SIAM J. Sci. Comput. 34(2), A889\u2013A913 (2012). https:\/\/doi.org\/10.1137\/100818583","journal-title":"SIAM J. Sci. Comput."},{"key":"1889_CR26","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1016\/j.cma.2016.04.025","volume":"307","author":"C Lehrenfeld","year":"2016","unstructured":"Lehrenfeld, C., Sch\u00f6berl, J.: High order exactly divergence-free hybrid discontinuous Galerkin methods for unsteady incompressible flows. Comput. Methods Appl. Mech. Eng. 307, 339\u2013361 (2016). https:\/\/doi.org\/10.1016\/j.cma.2016.04.025","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"7","key":"1889_CR27","doi-asserted-by":"publisher","first-page":"937","DOI":"10.1002\/mma.2849","volume":"37","author":"M Li","year":"2014","unstructured":"Li, M., Mao, S., Zhang, S.: New error estimates of nonconforming mixed finite element methods for the Stokes problem. Math. Methods Appl. Sci. 37(7), 937\u2013951 (2014). https:\/\/doi.org\/10.1002\/mma.2849","journal-title":"Math. Methods Appl. Sci."},{"key":"1889_CR28","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1553\/etna_vol52s281","volume":"52","author":"A Linke","year":"2020","unstructured":"Linke, A., Merdon, C., Neilan, M.: Pressure-robustness in quasi-optimal a priori estimates for the Stokes problem. Electron. Trans. Numer. Anal. 52, 281\u2013294 (2020). https:\/\/doi.org\/10.1553\/etna_vol52s281","journal-title":"Electron. Trans. Numer. Anal."},{"issue":"312","key":"1889_CR29","doi-asserted-by":"publisher","first-page":"1543","DOI":"10.1090\/mcom\/3344","volume":"87","author":"A Linke","year":"2018","unstructured":"Linke, A., Merdon, C., Neilan, M., Neumann, F.: Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes-problem. Math. Comput. 87(312), 1543\u20131566 (2018). https:\/\/doi.org\/10.1090\/mcom\/3344","journal-title":"Math. Comput."},{"issue":"4","key":"1889_CR30","doi-asserted-by":"publisher","first-page":"1982","DOI":"10.1137\/16M1083839","volume":"55","author":"S Rhebergen","year":"2017","unstructured":"Rhebergen, S., Wells, G.N.: Analysis of a hybridized\/interface stabilized finite element method for the Stokes equations. SIAM J. Numer. Anal. 55(4), 1982\u20132003 (2017). https:\/\/doi.org\/10.1137\/16M1083839","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"1889_CR31","doi-asserted-by":"publisher","first-page":"1484","DOI":"10.1007\/s10915-018-0671-4","volume":"76","author":"S Rhebergen","year":"2018","unstructured":"Rhebergen, S., Wells, G.N.: A hybridizable discontinuous Galerkin method for the Navier-Stokes equations with pointwise divergence-free velocity field. J. Sci. Comput. 76(3), 1484\u20131501 (2018). https:\/\/doi.org\/10.1007\/s10915-018-0671-4","journal-title":"J. Sci. Comput."},{"key":"1889_CR32","doi-asserted-by":"publisher","first-page":"112619","DOI":"10.1016\/j.cma.2019.112619","volume":"358","author":"S Rhebergen","year":"2020","unstructured":"Rhebergen, S., Wells, G.N.: An embedded-hybridized discontinuous Galerkin finite element method for the Stokes equations. Comput. Methods Appl. Mech. Eng. 358, 112619 (2020). https:\/\/doi.org\/10.1016\/j.cma.2019.112619","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1889_CR33","unstructured":"Sch\u00f6berl, J.: C++11 implementation of finite elements in NGSolve. Technical Report, ASC Report 30\/2014, Institute for Analysis and Scientific Computing, Vienna University of Technology (2014). https:\/\/www.asc.tuwien.ac.at\/~schoeberl\/wiki\/publications\/ngs-cpp11.pdf"},{"issue":"190","key":"1889_CR34","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1090\/S0025-5718-1990-1011446-7","volume":"54","author":"LR Scott","year":"1990","unstructured":"Scott, L.R., Zhang, S.: Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput. 54(190), 483\u2013493 (1990). https:\/\/doi.org\/10.1090\/S0025-5718-1990-1011446-7","journal-title":"Math. Comput."},{"key":"1889_CR35","doi-asserted-by":"publisher","unstructured":"Veeser, A., Zanotti, P.: Quasi-optimal nonconforming methods for second-order problems on domains with non-Lipschitz boundary. In: F.A. Radu, K.\u00a0Kumar, I.\u00a0Berre, J.M. Nordbotten, I.S. Pop (eds.) Numerical Mathematics and Advanced Applications ENUMATH 2017, pp. 461\u2013469. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-319-96415-7_41","DOI":"10.1007\/978-3-319-96415-7_41"},{"issue":"3","key":"1889_CR36","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/BF01390056","volume":"55","author":"R Verf\u00fcrth","year":"1989","unstructured":"Verf\u00fcrth, R.: A posteriori error estimators for the Stokes equations. Numer. Math. 55(3), 309\u2013325 (1989). https:\/\/doi.org\/10.1007\/BF01390056","journal-title":"Numer. Math."},{"issue":"3","key":"1889_CR37","doi-asserted-by":"publisher","first-page":"1082","DOI":"10.1137\/18M1177688","volume":"57","author":"R Verf\u00fcrth","year":"2019","unstructured":"Verf\u00fcrth, R., Zanotti, P.: A quasi-optimal Crouzeix-Raviart discretization of the Stokes equations. SIAM J. Numer. Anal. 57(3), 1082\u20131099 (2019). https:\/\/doi.org\/10.1137\/18M1177688","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"1889_CR38","doi-asserted-by":"publisher","first-page":"1269","DOI":"10.1137\/060649227","volume":"45","author":"J Wang","year":"2007","unstructured":"Wang, J., Ye, X.: New finite element methods in computational fluid dynamics by H(div) elements. SIAM J. Numer. Anal. 45(3), 1269\u20131286 (2007). https:\/\/doi.org\/10.1137\/060649227","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-022-01889-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-022-01889-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-022-01889-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T17:31:06Z","timestamp":1676050266000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-022-01889-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,3]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["1889"],"URL":"https:\/\/doi.org\/10.1007\/s10915-022-01889-6","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,3]]},"assertion":[{"value":"20 October 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 April 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 July 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}],"article-number":"51"}}