{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T08:21:14Z","timestamp":1789719674904,"version":"4.0.1"},"reference-count":49,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/100006751","name":"U.S. Army","doi-asserted-by":"publisher","award":["65294-MA"],"award-info":[{"award-number":["65294-MA"]}],"id":[{"id":"10.13039\/100006751","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS1522191"],"award-info":[{"award-number":["DMS1522191"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>This paper studies a new alteration of Yosida algebraic splitting methods for the Navier--Stokes equations. By applying the usual or pressure-corrected Yosida splitting techniques to discretizations written in terms of velocity and pressure updates $(u^{n+1}-u^n,p^{n+1}-p^n)$, we show that the accuracy is increased by one full order in $\\Delta t$ without any additional cost in the respective methods. Proofs of the convergence results are given both in linear algebraic and finite element frameworks. Several numerical tests are given which reveal the (sometimes dramatic) improvement in accuracy offered by the proposed fix.<\/jats:p>","DOI":"10.1137\/16m1061424","type":"journal-article","created":{"date-parts":[[2017,8,17]],"date-time":"2017-08-17T15:26:15Z","timestamp":1502983575000},"page":"A1489-A1513","source":"Crossref","is-referenced-by-count":18,"title":["Improved Accuracy in Algebraic Splitting Methods for Navier--Stokes Equations"],"prefix":"10.1137","volume":"39","author":[{"given":"Leo G.","family":"Rebholz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengying","family":"Xiao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,8,17]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/070680497"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/050646421"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2016.21.1027"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1002\/fld.4192"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1002\/fld.2495"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6715"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1002\/fld.1650080802"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-30728-0"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1968-0242392-2"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1002\/num.21752"},{"key":"atypb11","unstructured":"W. Couzy,\n                      Spectral Element Discretization of the Unsteady Navier-Stokes Equations and Its Iterative Solution on Parallel Computers\n                      , Ph.D. thesis, \u00c9cole Polytechnique f\u00e9d\u00e9rale de Lausanne, 1995."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199678792.001.0001"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-003-0114-z"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/070682800"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.09.018"},{"key":"atypb16","volume-title":"Incompressible Flow and the Finite Element Method","volume":"2","author":"Gresho P.","year":"1998"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2005.10.010"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/S0764-4442(01)02157-7"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901395400"},{"key":"atypb20","first-page":"1040","volume-title":"Proceedings from Finite Element Analysis in Fluids Conference","author":"Gunzburger M.","year":"1989"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1002\/num.20632"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1002\/fld.3654"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6907"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.01.019"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1002\/fld.679"},{"key":"atypb26","series-title":"SIAM Rev., to appear.","volume-title":"On the divergence constraint in mixed finite element methods for incompressible flows","author":"John V."},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2009.10.005"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1002\/fld.1461"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1137\/0907059"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1137\/15M1012311"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718904"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1002\/num.20281"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1063\/1.869966"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1007\/s00021-009-0299-0"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611973464"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1993.1162"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-663-11171-9"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1137\/07069609X"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-7824(99)00027-6"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903435429"},{"key":"atypb42","unstructured":"M. Sch$\\ddot{\\mbox{a}}$fer and S. Turek,\n                      The benchmark problem `flow around a cylinder,\n                      ' in Flow Simulation with High Performance Computers II, E.H. Hirschel, ed., Notes Numer. Fluid Mech., 52, Springer, Berlin, 1996, pp. 547-566."},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-96-00750-8"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1007\/BF00247696"},{"key":"atypb45","volume-title":"North-Holland","author":"Temam R.","year":"1991"},{"key":"atypb46","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0363(19960415)22:7<673::AID-FLD373>3.0.CO;2-O"},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-58393-3"},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1137\/080724484"},{"key":"atypb49","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2012.11.049"},{"key":"atypb50","unstructured":"U. Villa,\n                      Scalable Efficient Methods for Incompressible Fluid-Dynamics in Engineering Problems\n                      , Ph.D. thesis, Emory University, 2012."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1061424","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:58:12Z","timestamp":1787335092000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1061424"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":49,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1061424"],"URL":"https:\/\/doi.org\/10.1137\/16m1061424","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}