{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T03:30:14Z","timestamp":1787542214078,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-16-1-0102"],"award-info":[{"award-number":["FA9550-16-1-0102"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1620262"],"award-info":[{"award-number":["DMS-1620262"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1720442"],"award-info":[{"award-number":["DMS-1720442"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We carry out convergence and error analysis of the scalar auxiliary variable (SAV) methods for $L^2$ and $H^{-1}$ gradient flows with a typical form of free energy. We first derive $H^2$ bounds, under certain assumptions suitable for both the gradient flows and the SAV schemes, which allow us to establish the convergence of the SAV schemes under mild conditions. We then derive error estimates with further regularity assumptions. We also discuss several other gradient flows, which cannot be cast in the general framework used in this paper, but for which convergence and error analysis can still be established using a similar procedure.<\/jats:p>","DOI":"10.1137\/17m1159968","type":"journal-article","created":{"date-parts":[[2018,9,25]],"date-time":"2018-09-25T11:14:51Z","timestamp":1537874091000},"page":"2895-2912","source":"Crossref","is-referenced-by-count":346,"title":["Convergence and Error Analysis for the  Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows"],"prefix":"10.1137","volume":"56","author":[{"given":"Jie","family":"Shen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jie","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,9,25]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0001-6160(79)90196-2"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/120880677"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202514500407"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1063\/1.1744102"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-10-02365-3"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1080\/15421407108082773"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/0728069"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.70.051605"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/0730084"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-002-0413-1"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-004-0546-5"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2012.09.020"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2004006"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1017\/S095679250300528X"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.79.1261"},{"key":"atypb16","volume-title":"Numerical Approximation of Partial Differential Equations","author":"Quarteroni A.","year":"2008"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.10.021"},{"key":"atypb18","series-title":"SIAM Rev., to appear","volume-title":"A new class of efficient and robust energy stable schemes for gradient flows","author":"Shen J."},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/s11401-010-0599-y"},{"key":"atypb20","volume-title":"North-Holland","author":"Temam R.","year":"1984"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0645-3"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.09.029"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(02)00566-6"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1159968","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:40:49Z","timestamp":1787326849000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1159968"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":23,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1159968"],"URL":"https:\/\/doi.org\/10.1137\/17m1159968","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}