{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T09:01:35Z","timestamp":1776070895149,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,3,8]],"date-time":"2023-03-08T00:00:00Z","timestamp":1678233600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,3,8]],"date-time":"2023-03-08T00:00:00Z","timestamp":1678233600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"the NSF of China","award":["No.12001466"],"award-info":[{"award-number":["No.12001466"]}]},{"name":"the NSF of China","award":["No. U19A2079"],"award-info":[{"award-number":["No. U19A2079"]}]},{"name":"the NSF of China","award":["No. 11671345"],"award-info":[{"award-number":["No. 11671345"]}]},{"name":"the Research Fund from Key Laboratory of Xinjiang Province","award":["No. 2020D04002"],"award-info":[{"award-number":["No. 2020D04002"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2023,4]]},"DOI":"10.1007\/s10915-023-02150-4","type":"journal-article","created":{"date-parts":[[2023,3,8]],"date-time":"2023-03-08T05:03:00Z","timestamp":1678251780000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["An Adaptive Time-Stepping Method for the Binary Fluid-Surfactant Phase Field Model on Evolving Surfaces"],"prefix":"10.1007","volume":"95","author":[{"given":"Shijie","family":"Huang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0716-2593","authenticated-orcid":false,"given":"Xufeng","family":"Xiao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinlong","family":"Feng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,3,8]]},"reference":[{"issue":"6","key":"2150_CR1","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1007\/s00285-011-0401-0","volume":"63","author":"R Barreira","year":"2011","unstructured":"Barreira, R., Elliott, C.M., Madzvamuse, A.: The surface finite element method for pattern formation on evolving biological surfaces. J. Math. Biol. 63(6), 1095\u20131119 (2011)","journal-title":"J. Math. Biol."},{"issue":"5","key":"2150_CR2","doi-asserted-by":"crossref","first-page":"2677","DOI":"10.1137\/110828642","volume":"50","author":"G Dziuk","year":"2012","unstructured":"Dziuk, G., Elliott, C.M.: A fully discrete evolving surface finite element method. SIAM J. Numer. Anal. 50(5), 2677\u20132694 (2012)","journal-title":"SIAM J. Numer. Anal."},{"key":"2150_CR3","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1017\/S0962492913000056","volume":"22","author":"G Dziuk","year":"2013","unstructured":"Dziuk, G., Elliott, C.M.: Finite element methods for surface PDEs. Acta Numer. 22, 289\u2013396 (2013)","journal-title":"Acta Numer."},{"issue":"2","key":"2150_CR4","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1093\/imanum\/drl023","volume":"27","author":"G Dziuk","year":"2007","unstructured":"Dziuk, G., Elliott, C.M.: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27(2), 262\u2013292 (2007)","journal-title":"IMA J. Numer. Anal."},{"issue":"2","key":"2150_CR5","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1093\/imanum\/drr017","volume":"32","author":"G Dziuk","year":"2012","unstructured":"Dziuk, G., Lubich, C., Mansour, D.: Runge\u2013Kutta time discretization of parabolic differential equations on evolving surfaces. IMA J. Numer. Anal. 32(2), 394\u2013416 (2012)","journal-title":"IMA J. Numer. Anal."},{"issue":"3","key":"2150_CR6","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/s00211-014-0644-y","volume":"129","author":"CM Elliott","year":"2015","unstructured":"Elliott, C.M., Ranner, T.: Evolving surface finite element method for the Cahn\u2013Hilliard equation. Numer. Math. 129(3), 483\u2013534 (2015)","journal-title":"Numer. Math."},{"issue":"4","key":"2150_CR7","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.87.048302","volume":"87","author":"CD Eggleton","year":"2001","unstructured":"Eggleton, C.D., Tsai, T.M., Stebe, K.J.: Tip streaming from a drop in the presence of surfactants. Phys. Rev. Lett. 87(4), 048302 (2001)","journal-title":"Phys. Rev. Lett."},{"issue":"3","key":"2150_CR8","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1007\/s00205-006-0012-x","volume":"183","author":"I Fonseca","year":"2007","unstructured":"Fonseca, I., Morini, M., Slastikov, V.: Surfactants in foam stability: a phase-field model. Arch. Ration. Mech. Anal. 183(3), 411\u2013456 (2007)","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"1","key":"2150_CR9","doi-asserted-by":"crossref","first-page":"59","DOI":"10.4208\/eajam.200113.220213a","volume":"3","author":"X Feng","year":"2013","unstructured":"Feng, X., Tang, T., Yang, J.: Stabilized Crank\u2013Nicolson\/Adams\u2013Bashforth schemes for phase field models. East Asian J. Appl. Math. 3(1), 59\u201380 (2013)","journal-title":"East Asian J. Appl. Math."},{"key":"2150_CR10","unstructured":"Gompper, G.: Self-assembling amphiphilic systems. Phase Transit Crit Phenomena 16 (1994)"},{"key":"2150_CR11","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1016\/j.jcp.2014.03.060","volume":"270","author":"S Gu","year":"2014","unstructured":"Gu, S., Zhang, H., Zhang, Z.: An energy-stable finite-difference scheme for the binary fluid-surfactant system. J. Comput. Phys. 270, 416\u2013431 (2014)","journal-title":"J. Comput. Phys."},{"key":"2150_CR12","doi-asserted-by":"crossref","DOI":"10.1016\/j.amc.2022.127622","volume":"439","author":"S Huang","year":"2023","unstructured":"Huang, S., Xiao, X., Feng, X.: An adaptive time-stepping method for the phase-field molecular beam epitaxial growth model on evolving surfaces. Appl. Math. Comput. 439, 127622 (2023)","journal-title":"Appl. Math. Comput."},{"issue":"3","key":"2150_CR13","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1063\/1.870254","volume":"12","author":"YT Hu","year":"2000","unstructured":"Hu, Y.T., Pine, D.J., Leal, L.G.: Drop deformation, breakup, and coalescence with compatibilizer. Phys. Fluids 12(3), 484\u2013489 (2000)","journal-title":"Phys. Fluids"},{"key":"2150_CR14","unstructured":"Hou, D., Qiao, Z.: A linear adaptive BDF2 scheme for phase field crystal equation. ArXiv Preprint arXiv:2206.07625 (2022)"},{"key":"2150_CR15","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.cma.2015.05.010","volume":"293","author":"P Hansbo","year":"2015","unstructured":"Hansbo, P., Larson, M.G., Zahedi, S.: Characteristic cut finite element methods for convection-diffusion problems on time dependent surfaces. Comput. Methods Appl. Mech. Eng. 293, 431\u2013461 (2015)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"2150_CR16","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s003710050126","volume":"14","author":"E Hartmann","year":"1998","unstructured":"Hartmann, E.: A marching method for the triangulation of surfaces. Vis. Comput. 14(3), 95\u2013108 (1998)","journal-title":"Vis. Comput."},{"issue":"4","key":"2150_CR17","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1093\/imanum\/23.4.665","volume":"23","author":"Y He","year":"2003","unstructured":"He, Y.: A fully discrete stabilized finite-element method for the time-dependent Navier\u2013Stokes problem. IMA J. Numer. Anal. 23(4), 665\u2013691 (2003)","journal-title":"IMA J. Numer. Anal."},{"issue":"2","key":"2150_CR18","doi-asserted-by":"crossref","first-page":"1722","DOI":"10.1103\/PhysRevE.55.1722","volume":"55","author":"S Komura","year":"1997","unstructured":"Komura, S., Kodama, H.: Two-order-parameter model for an oil-water-surfactant system. Phys. Rev. E 55(2), 1722 (1997)","journal-title":"Phys. Rev. E"},{"issue":"1","key":"2150_CR19","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1093\/imanum\/draa075","volume":"42","author":"HL Liao","year":"2022","unstructured":"Liao, H.L., Ji, B., Zhang, L.: An adaptive BDF2 implicit time-stepping method for the phase field crystal model. IMA J. Numer. Anal. 42(1), 649\u2013679 (2022)","journal-title":"IMA J. Numer. Anal."},{"issue":"2","key":"2150_CR20","first-page":"1","volume":"92","author":"HL Liao","year":"2022","unstructured":"Liao, H.L., Ji, B., Wang, L., Zhang, Z.: Mesh-robustness of an energy stable BDF2 scheme with variable steps for the Cahn\u2013Hilliard model. J. Sci. Comput. 92(2), 1\u201326 (2022)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"2150_CR21","doi-asserted-by":"crossref","first-page":"1643","DOI":"10.1137\/17M1148633","volume":"56","author":"C Lehrenfeld","year":"2018","unstructured":"Lehrenfeld, C., Olshanskii, M.A., Xu, X.: A stabilized trace finite element method for partial differential equations on evolving surfaces. SIAM J. Numer. Anal. 56(3), 1643\u20131672 (2018)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"2150_CR22","doi-asserted-by":"crossref","first-page":"A2129","DOI":"10.1137\/16M1095457","volume":"39","author":"E Lehto","year":"2017","unstructured":"Lehto, E., Shankar, V., Wright, G.B.: A radial basis function (RBF) compact finite difference (FD) scheme for reaction-diffusion equations on surfaces. SIAM J. Sci. Comput. 39(5), A2129\u2013A2151 (2017)","journal-title":"SIAM J. Sci. Comput."},{"issue":"32","key":"2150_CR23","doi-asserted-by":"crossref","first-page":"6715","DOI":"10.1088\/0953-8984\/4\/32\/006","volume":"4","author":"M Laradji","year":"1992","unstructured":"Laradji, M., Guo, H., Grant, M., Zuckermann, M.J.: The effect of surfactants on the dynamics of phase separation. J. Phys. Condens. Matter 4(32), 6715 (1992)","journal-title":"J. Phys. Condens. Matter"},{"issue":"8","key":"2150_CR24","doi-asserted-by":"crossref","first-page":"1855","DOI":"10.1016\/j.camwa.2017.02.021","volume":"73","author":"Y Li","year":"2017","unstructured":"Li, Y., Choi, Y., Kim, J.: Computationally efficient adaptive time step method for the Cahn\u2013Hilliard equation. Comput. Math. Appl. 73(8), 1855\u20131864 (2017)","journal-title":"Comput. Math. Appl."},{"issue":"2","key":"2150_CR25","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s10915-008-9196-6","volume":"35","author":"CB Macdonald","year":"2008","unstructured":"Macdonald, C.B., Ruuth, S.J.: Level set equations on surfaces via the closest point method. J. Sci. Comput. 35(2), 219\u2013240 (2008)","journal-title":"J. Sci. Comput."},{"issue":"6","key":"2150_CR26","doi-asserted-by":"crossref","first-page":"4330","DOI":"10.1137\/080740003","volume":"31","author":"CB Macdonald","year":"2010","unstructured":"Macdonald, C.B., Ruuth, S.J.: The implicit closest point method for the numerical solution of partial differential equations on surfaces. SIAM J. Sci. Comput. 31(6), 4330\u20134350 (2010)","journal-title":"SIAM J. Sci. Comput."},{"key":"2150_CR27","unstructured":"O\u2019Connor, D.: Phase field models on evolving surfaces. University of Warwick (2016)"},{"key":"2150_CR28","doi-asserted-by":"crossref","unstructured":"Olshanskii, M.A., Reusken, A.: Trace finite element methods for PDEs on surfaces. Geometrically Unfitted Finite Element Methods and Applications, pp. 211\u2013258 (2017)","DOI":"10.1007\/978-3-319-71431-8_7"},{"issue":"4","key":"2150_CR29","doi-asserted-by":"crossref","first-page":"A1301","DOI":"10.1137\/16M1099388","volume":"39","author":"MA Olshanskii","year":"2017","unstructured":"Olshanskii, M.A., Xu, X.: A trace finite element method for PDEs on evolving surfaces. SIAM J. Sci. Comput. 39(4), A1301\u2013A1319 (2017)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"2150_CR30","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1137\/S0036144503429121","volume":"46","author":"PO Persson","year":"2004","unstructured":"Persson, P.O., Strang, G.: A simple mesh generator in MATLAB. SIAM Rev. 46(2), 329\u2013345 (2004)","journal-title":"SIAM Rev."},{"key":"2150_CR31","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.jcp.2018.12.031","volume":"381","author":"A Petras","year":"2019","unstructured":"Petras, A., Ling, L., Piret, C., Ruuth, S.J.: A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces. J. Comput. Phys. 381, 146\u2013161 (2019)","journal-title":"J. Comput. Phys."},{"key":"2150_CR32","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.jcp.2018.05.022","volume":"370","author":"A Petras","year":"2018","unstructured":"Petras, A., Ling, L., Ruuth, S.J.: An RBF-FD closest point method for solving PDEs on surfaces. J. Comput. Phys. 370, 43\u201357 (2018)","journal-title":"J. Comput. Phys."},{"key":"2150_CR33","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.jcp.2016.02.024","volume":"312","author":"A Petras","year":"2016","unstructured":"Petras, A., Ruuth, S.J.: PDEs on moving surfaces via the closest point method and a modified grid based particle method. J. Comput. Phys. 312, 139\u2013156 (2016)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"2150_CR34","doi-asserted-by":"crossref","first-page":"1943","DOI":"10.1016\/j.jcp.2007.10.009","volume":"227","author":"SJ Ruuth","year":"2008","unstructured":"Ruuth, S.J., Merriman, B.: A simple embedding method for solving partial differential equations on surfaces. J. Comput. Phys. 227(3), 1943\u20131961 (2008)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"2150_CR35","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1007\/s10915-014-9914-1","volume":"63","author":"V Shankar","year":"2015","unstructured":"Shankar, V., Wright, G.B., Kirby, R.M., Fogelson, A.L.: A radial basis function (RBF)-finite difference (FD) method for diffusion and reaction-diffusion equations on surfaces. J. Sci. Comput. 63(3), 745\u2013768 (2015)","journal-title":"J. Sci. Comput."},{"issue":"4","key":"2150_CR36","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1080\/00036819008839963","volume":"38","author":"J Shen","year":"1990","unstructured":"Shen, J.: Long time stability and convergence for fully discrete nonlinear Galerkin methods. Appl. Anal. 38(4), 201\u2013229 (1990)","journal-title":"Appl. Anal."},{"key":"2150_CR37","volume":"367","author":"M Sun","year":"2020","unstructured":"Sun, M., Feng, X., Wang, K.: Numerical simulation of binary fluid-surfactant phase field model coupled with geometric curvature on the curved surface. Comput. Methods Appl. Mech. Eng. 367, 113123 (2020)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2150_CR38","volume":"111","author":"H Sun","year":"2022","unstructured":"Sun, H., Zhao, X., Cao, H., Yang, R., Zhang, M.: Stability and convergence analysis of adaptive BDF2 scheme for the Swift-Hohenberg equation. Commun. Nonlinear Sci. Numer. Simul. 111, 106412 (2022)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"4","key":"2150_CR39","first-page":"1289","volume":"17","author":"CH Teng","year":"2012","unstructured":"Teng, C.H., Chern, I.L., Lai, M.C.: Simulating binary fluid-surfactant dynamics by a phase field model. Discrete Contin. Dyn. Syst.-B 17(4), 1289 (2012)","journal-title":"Discrete Contin. Dyn. Syst.-B"},{"key":"2150_CR40","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1006\/jcis.2000.7349","volume":"235","author":"T Teramoto","year":"2001","unstructured":"Teramoto, T., Yonezawa, F.: Droplet growth dynamics in a water\/oil\/surfactant system. J. Colloid Interface Sci. 235, 329\u2013333 (2001)","journal-title":"J. Colloid Interface Sci."},{"key":"2150_CR41","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s00397-005-0081-z","volume":"46","author":"RGM Van der Sman","year":"2006","unstructured":"Van der Sman, R.G.M., Van der Graaf, S.: Diffuse interface model of surfactant adsorption onto flat and droplet interfaces. Rheol. Acta 46, 3\u201311 (2006)","journal-title":"Rheol. Acta"},{"key":"2150_CR42","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1016\/j.cma.2017.02.011","volume":"318","author":"X Yang","year":"2017","unstructured":"Yang, X., Ju, L.: Linear and unconditionally energy stable schemes for the binary fluid-surfactant phase field model. Comput. Methods Appl. Mech. Eng. 318, 1005\u20131029 (2017)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"2150_CR43","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1007\/s10915-017-0508-6","volume":"74","author":"X Yang","year":"2018","unstructured":"Yang, X.: Numerical approximations for the Cahn\u2013Hilliard phase field model of the binary fluid-surfactant system. J. Sci. Comput. 74(3), 1533\u20131553 (2018)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"2150_CR44","doi-asserted-by":"crossref","first-page":"B479","DOI":"10.1137\/20M1336734","volume":"43","author":"X Yang","year":"2021","unstructured":"Yang, X.: On a novel fully decoupled, second-order accurate energy stable numerical scheme for a binary fluid-surfactant phase-field model. SIAM J. Sci. Comput. 43(2), B479\u2013B507 (2021)","journal-title":"SIAM J. Sci. Comput."},{"key":"2150_CR45","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.cpc.2018.07.003","volume":"233","author":"G Zhu","year":"2018","unstructured":"Zhu, G., Kou, J., Sun, S., Yao, J., Li, A.: Decoupled, energy stable schemes for a phase-field surfactant model. Comput. Phys. Commun. 233, 67\u201377 (2018)","journal-title":"Comput. Phys. Commun."},{"issue":"3","key":"2150_CR46","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10444-020-09793-z","volume":"46","author":"J Zhang","year":"2020","unstructured":"Zhang, J., Yang, X.: Non-iterative, unconditionally energy stable and large time-stepping method for the Cahn\u2013Hilliard phase-field model with Flory-Huggins-de Gennes free energy. Adv. Comput. Math. 46(3), 1\u201327 (2020)","journal-title":"Adv. Comput. Math."},{"issue":"4","key":"2150_CR47","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.4208\/cicp.300810.140411s","volume":"11","author":"Z Zhang","year":"2012","unstructured":"Zhang, Z., Qiao, Z.: An adaptive time-stepping strategy for the Cahn\u2013Hilliard equation. Commun. Comput. Phys. 11(4), 1261\u20131278 (2012)","journal-title":"Commun. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02150-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-023-02150-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02150-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,8]],"date-time":"2023-12-08T13:51:54Z","timestamp":1702043514000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-023-02150-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,8]]},"references-count":47,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["2150"],"URL":"https:\/\/doi.org\/10.1007\/s10915-023-02150-4","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,8]]},"assertion":[{"value":"9 September 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 January 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 February 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 March 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"No conflict of interest exists in the submission of this manuscript, and the manuscript is approved by all authors for publication.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"29"}}