{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T11:49:00Z","timestamp":1777981740808,"version":"3.51.4"},"reference-count":67,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["12171415"],"award-info":[{"award-number":["12171415"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["12271468"],"award-info":[{"award-number":["12271468"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"crossref","award":["DMS-1818642"],"award-info":[{"award-number":["DMS-1818642"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"crossref","award":["DMS-1818783"],"award-info":[{"award-number":["DMS-1818783"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"crossref","award":["DMS-2012490"],"award-info":[{"award-number":["DMS-2012490"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,6,30]]},"DOI":"10.1137\/22m1499376","type":"journal-article","created":{"date-parts":[[2023,6,1]],"date-time":"2023-06-01T20:03:49Z","timestamp":1685649829000},"page":"B253-B282","source":"Crossref","is-referenced-by-count":27,"title":["Reformulated Weak Formulation and Efficient Fully Discrete Finite Element Method for a Two-Phase Ferrohydrodynamics Shliomis Model"],"prefix":"10.1137","volume":"45","author":[{"given":"Guo-dong","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Sciences, Yantai University, Yantai, 264005, Shandong, People\u2019s Republic of China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1270-4972","authenticated-orcid":true,"given":"Xiaoming","family":"He","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Missouri University of Science & Technology, Rolla, MO 65409 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofeng","family":"Yang","sequence":"additional","affiliation":[{"name":"Corresponding author. Department of Mathematics, University of South Carolina, Columbia, SC 29208 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"351","published-online":{"date-parts":[[2023,6,1]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s10665-017-9931-9"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/19M1264412"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/120880677"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1021\/la5009939"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.101111.110512a"},{"key":"ref7","first-page":"839","volume":"19","author":"Chen X.","year":"2022","journal-title":"Int. J. Numer. Anal. Model."},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.2019.js60.10"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.04.010"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2019.60"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2015.01.053"},{"key":"ref12","first-page":"85","volume":"19","author":"Fei J.","year":"2022","journal-title":"Int. J. Numer. Anal. Model."},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.110968"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/16M1100885"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1002\/num.22829"},{"key":"ref16","doi-asserted-by":"crossref","unstructured":"V. Girault and P. A. Raviart , Finite Element Method for Navier-Stokes Equations: Theory and Algorithms, Springer-Verlag, Berlin, Heidelberg, 1987, pp. 395\u2013414.","DOI":"10.1007\/978-3-642-61623-5"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112006003466"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2005.10.010"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.05.055"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-015-0055-y"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.02.046"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.98.033301"},{"key":"ref23","doi-asserted-by":"crossref","first-page":"2177","DOI":"10.3934\/dcdsb.2017209","volume":"23","author":"Huang Q.","year":"2018","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.4171\/IFB\/178"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/17M1162287"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-020-09764-4"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1063\/1.3618737"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2019.06.007"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(03)00030-7"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.4028\/www.scientific.net\/AMR.433-440.3767"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmmm.2006.10.1174"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1007\/s10404-011-0903-5"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2016.06.011"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmmm.2011.06.016"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.2019.js60.06"},{"key":"ref36","first-page":"399","volume":"18","author":"Qin Y.","year":"2021","journal-title":"Int. J. Numer. Anal. Model."},{"key":"ref37","volume-title":"Ferrohydrodynamics","author":"Rosensweig R. E.","year":"1985"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.fl.19.010187.002253"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-96-00750-8"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1137\/110822839"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1137\/17M1150153"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2010.28.1669"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1137\/130921593"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1137\/140971154"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/754\/15147"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijthermalsci.2010.05.021"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1263\/jbb.100.1"},{"key":"ref48","first-page":"1291","volume":"34","author":"Shliomis M. I.","year":"1972","journal-title":"Sov. phys. JETP"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45646-5_5"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmmm.2017.11.090"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.4310\/CMS.2019.v17.n3.a10"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.OA-2016-0197"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.07.022"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.110015"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1137\/20M1336734"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2021.114376"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.111448"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2017.02.011"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1137\/17M1125005"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-020-01151-x"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2018.04.027"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112004000370"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmmm.2013.07.021"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110752"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1137\/19M1288280"},{"key":"ref66","first-page":"642","volume":"18","author":"Zhang H.","year":"2021","journal-title":"Int. J. Numer. Anal. Model."},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2017.01.031"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","deposited":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T17:47:40Z","timestamp":1729532860000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1499376"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,1]]},"references-count":67,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,6,30]]}},"alternative-id":["10.1137\/22M1499376"],"URL":"https:\/\/doi.org\/10.1137\/22m1499376","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,1]]}}}