{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:53Z","timestamp":1787337293880,"version":"build-2736575974"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>Least\u2010squares variational methods have several practical and theoretical advantages for solving elliptic partial differential equations, including symmetric positive definite discrete operators and a sharp error measure. One of the potential drawbacks, especially in three dimensions, is that mass conservation is achieved only in a least\u2010squares sense, and underresolved solutions are especially vulnerable to poor conservation. For the stationary Navier\u2013Stokes equations, which are typically rewritten as a larger system of first\u2010order equations, the loss of mass in the approximate solution is strongly dependent upon the boundary conditions used. A new first\u2010order system reformulation of the Navier\u2013Stokes equations is presented that admits a wider range of mass\u2010conserving boundary conditions. This new formulation is shown to provide both excellent mass conservation and excellent algebraic multigrid performance for three different problems, a square channel, backward\u2010facing step, and branching tubes with two generations of bifurcations.<\/jats:p>","DOI":"10.1137\/050640928","type":"journal-article","created":{"date-parts":[[2006,10,23]],"date-time":"2006-10-23T11:31:00Z","timestamp":1161603060000},"page":"1675-1693","source":"Crossref","is-referenced-by-count":28,"title":["On Mass\u2010Conserving Least\u2010Squares Methods"],"prefix":"10.1137","volume":"28","author":[{"given":"J. J.","family":"Heys","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E.","family":"Lee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T. A.","family":"Manteuffel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S. F.","family":"Mccormick","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112083002839"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1002\/nla.373"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994276001"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142996313592"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7930(93)90025-5"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144597321156"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997324976"},{"key":"R8","first-page":"110","volume":"201","author":"Bolton P.","year":"2004","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"W. L. Briggs, V. E. Henson, and S. F. McCormick,\n                      A Multigrid Tutorial\n                      , 2nd ed., SIAM, Philadelphia, 2000.","DOI":"10.1137\/1.9780898719505"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903422673"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142900388049"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994266066"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539794273368"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142902404406"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142902404418"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595294526"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"R. D. Falgout and U. M. Yang,\n                      hypre: A library of high performance preconditioners\n                      , in Computational Science\u2014ICCS 2002, Part III, Lecture Notes in Comput. Sci. 2331, Springer\u2010Verlag, Berlin, 2002, pp. 632\u2013641.","DOI":"10.1007\/3-540-47789-6_66"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1002\/fld.1650110702"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.09.034"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2004.10.021"},{"key":"R21","doi-asserted-by":"crossref","unstructured":"B. N. Jiang,\n                      The Least\u2010Squares Finite Element Method\n                      , Springer\u2010Verlag, Berlin, 1998.","DOI":"10.1007\/978-3-662-03740-9"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1080\/10618569508904515"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595287997"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.11.030"},{"key":"R25","unstructured":"O. R\u00f6hrle,\n                      Multilevel First\u2010Order System Least Squares for Quasilinear Elliptic Partial Differential Equations\n                      , Ph.D. thesis, Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO, 2004."},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1002\/fld.1650170402"},{"key":"R27","unstructured":"F. M. White,\n                      Viscous Fluid Flow\n                      , 2nd ed., McGraw\u2010Hill, New York, 1991."},{"key":"R28","unstructured":"F. M. White,\n                      Fluid Mechanics\n                      , 5th ed., McGraw\u2010Hill, Boston, MA, 2003."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/050640928","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:55:05Z","timestamp":1787334905000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/050640928"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":28,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/050640928"],"URL":"https:\/\/doi.org\/10.1137\/050640928","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}