{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,20]],"date-time":"2022-12-20T16:38:47Z","timestamp":1671554327295},"reference-count":8,"publisher":"American Mathematical Society (AMS)","issue":"268","license":[{"start":{"date-parts":[[2010,2,16]],"date-time":"2010-02-16T00:00:00Z","timestamp":1266278400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

A symmetric error estimate for Galerkin approximations of solutions of the Navier-Stokes equations in two space dimensions plus time is given. The finite-dimensional function spaces are taken to be divergence-free, and time is left continuous. The estimate is similar to known results for scalar parabolic equations. An application of the result is given for mixed method formulations. A short discussion of examples is included. Finally, there are some remarks about a partial extension to three space dimensions.<\/p>","DOI":"10.1090\/s0025-5718-09-02243-1","type":"journal-article","created":{"date-parts":[[2009,6,30]],"date-time":"2009-06-30T14:39:02Z","timestamp":1246372742000},"page":"1919-1927","source":"Crossref","is-referenced-by-count":2,"title":["A symmetric error estimate for Galerkin approximations of time-dependent Navier-Stokes equations in two dimensions"],"prefix":"10.1090","volume":"78","author":[{"given":"Todd","family":"Dupont","sequence":"first","affiliation":[]},{"given":"Itir","family":"Mogultay","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2009,2,16]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/0730001","article-title":"Analysis of some moving space-time finite element methods","volume":"30","author":"Bank, Randolph E.","year":"1993","journal-title":"SIAM J. Numer. Anal.","ISSN":"http:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"2","series-title":"Texts in Applied Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0","volume-title":"The mathematical theory of finite element methods","volume":"15","author":"Brenner, Susanne C.","year":"2008","ISBN":"http:\/\/id.crossref.org\/isbn\/9780387759333","edition":"3"},{"key":"3","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1137\/0707048","article-title":"Galerkin methods for parabolic equations","volume":"7","author":"Douglas, Jim, Jr.","year":"1970","journal-title":"SIAM J. Numer. Anal.","ISSN":"http:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"159","key":"4","doi-asserted-by":"publisher","first-page":"85","DOI":"10.2307\/2007621","article-title":"Mesh modification for evolution equations","volume":"39","author":"Dupont, Todd","year":"1982","journal-title":"Math. Comp.","ISSN":"http:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"3","key":"5","doi-asserted-by":"publisher","first-page":"914","DOI":"10.1137\/S0036142900380431","article-title":"Symmetric error estimates for moving mesh Galerkin methods for advection-diffusion equations","volume":"40","author":"Dupont, Todd F.","year":"2002","journal-title":"SIAM J. Numer. Anal.","ISSN":"http:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"6","volume-title":"Quelques m\\'{e}thodes de r\\'{e}solution des probl\\`emes aux limites non lin\\'{e}aires","author":"Lions, J.-L.","year":"1969"},{"key":"7","unstructured":"I. Mogultay, T. F. Dupont, and G. Eshel, Dimension reduction applied to a model of sea breezes, Tech. report, U. of Chicago, Dept. of Computer Science, TR-2007-06."},{"key":"8","series-title":"Studies in Mathematics and its Applications","isbn-type":"print","volume-title":"Navier-Stokes equations","volume":"2","author":"Temam, Roger","year":"1984","ISBN":"http:\/\/id.crossref.org\/isbn\/0444875581","edition":"3"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2009-78-268\/S0025-5718-09-02243-1\/S0025-5718-09-02243-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-268\/S0025-5718-09-02243-1\/S0025-5718-09-02243-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,30]],"date-time":"2021-07-30T03:39:21Z","timestamp":1627616361000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-268\/S0025-5718-09-02243-1\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,2,16]]},"references-count":8,"journal-issue":{"issue":"268","published-print":{"date-parts":[[2009,10]]}},"alternative-id":["S0025-5718-09-02243-1"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-09-02243-1","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["0025-5718","1088-6842"],"issn-type":[{"value":"0025-5718","type":"print"},{"value":"1088-6842","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,2,16]]}}}