{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T07:21:48Z","timestamp":1774509708582,"version":"3.50.1"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T00:00:00Z","timestamp":1635724800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T00:00:00Z","timestamp":1635724800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2021,11]]},"DOI":"10.1007\/s00211-021-01238-z","type":"journal-article","created":{"date-parts":[[2021,11,5]],"date-time":"2021-11-05T13:02:57Z","timestamp":1636117377000},"page":"595-643","update-policy":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":42,"title":["A convergent evolving finite element algorithm for Willmore flow of closed surfaces"],"prefix":"10.1007","volume":"149","author":[{"given":"Bal\u00e1zs","family":"Kov\u00e1cs","sequence":"first","affiliation":[]},{"given":"Buyang","family":"Li","sequence":"additional","affiliation":[]},{"given":"Christian","family":"Lubich","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,5]]},"reference":[{"issue":"4","key":"1238_CR1","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1093\/imanum\/drs041","volume":"33","author":"S Bartels","year":"2013","unstructured":"Bartels, S.: A simple scheme for the approximation of the elastic flow of inextensible curves. IMA J. Numer. Anal. 33(4), 1115\u20131125 (2013)","journal-title":"IMA J. Numer. Anal."},{"issue":"1","key":"1238_CR2","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1016\/j.jcp.2006.07.026","volume":"222","author":"JW Barrett","year":"2007","unstructured":"Barrett, J.W., Garcke, H., N\u00fcrnberg, R.: A parametric finite element method for fourth order geometric evolution equations. J. Comput. Phys. 222(1), 441\u2013467 (2007)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"1238_CR3","doi-asserted-by":"publisher","first-page":"1006","DOI":"10.1137\/060653974","volume":"29","author":"JW Barrett","year":"2007","unstructured":"Barrett, J.W., Garcke, H., N\u00fcrnberg, R.: On the variational approximation of combined second and fourth order geometric evolution equations. SIAM J. Sci. Comput. 29(3), 1006\u20131041 (2007)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"1238_CR4","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1137\/070700231","volume":"31","author":"JW Barrett","year":"2008","unstructured":"Barrett, J.W., Garcke, H., N\u00fcrnberg, R.: Parametric approximation of Willmore flow and related geometric evolution equations. SIAM J. on Sci. Comput. 31(1), 225\u2013253 (2008)","journal-title":"SIAM J. on Sci. Comput."},{"issue":"5","key":"1238_CR5","doi-asserted-by":"publisher","first-page":"052704","DOI":"10.1103\/PhysRevE.92.052704","volume":"92","author":"JW Barrett","year":"2015","unstructured":"Barrett, J.W., Garcke, H., N\u00fcrnberg, R.: Numerical computations of the dynamics of fluidic membranes and vesicles. Phys. Rev. E 92(5), 052704 (2015)","journal-title":"Phys. Rev. E"},{"key":"1238_CR6","doi-asserted-by":"crossref","unstructured":"Barrett, J.W., Garcke, H., N\u00fcrnberg, R.: Parametric finite element approximations of curvature driven interface evolutions. In: Handbook of Numerical Analysis vol. 21, pp. 275\u2013423 (2020)","DOI":"10.1016\/bs.hna.2019.05.002"},{"issue":"6","key":"1238_CR7","doi-asserted-by":"publisher","first-page":"2093","DOI":"10.1137\/16M1091599","volume":"77","author":"W Bao","year":"2017","unstructured":"Bao, W., Jiang, W., Srolovitz, D.J., Wang, Y.: Stable equilibria of anisotropic particles on substrates: a generalized Winterbottom construction. SIAM J. Appl. Math. 77(6), 2093\u20132118 (2017)","journal-title":"SIAM J. Appl. Math."},{"key":"1238_CR8","doi-asserted-by":"publisher","first-page":"380","DOI":"10.1016\/j.jcp.2016.11.015","volume":"330","author":"W Bao","year":"2017","unstructured":"Bao, W., Jiang, W., Wang, Y., Zhao, Q.: A parametric finite element method for solid-state dewetting problems with anisotropic surface energies. J. Comput. Phys. 330, 380\u2013400 (2017)","journal-title":"J. Comput. Phys."},{"key":"1238_CR9","volume-title":"Vorlesungen \u00fcber Differentialgeometrie III. Grundlehren der mathematischen Wissenschaften","author":"W Blaschke","year":"1929","unstructured":"Blaschke, W.: Vorlesungen \u00fcber Differentialgeometrie III. Grundlehren der mathematischen Wissenschaften. Springer, Berlin (1929)"},{"issue":"2","key":"1238_CR10","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1137\/S0036142902419272","volume":"42","author":"E B\u00e4nsch","year":"2004","unstructured":"B\u00e4nsch, E., Morin, P., Nochetto, R.H.: Surface diffusion of graphs: variational formulation, error analysis, and simulation. SIAM J. Numer. Anal. 42(2), 773\u2013799 (2004)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"1238_CR11","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/j.jcp.2004.08.022","volume":"203","author":"E B\u00e4nsch","year":"2005","unstructured":"B\u00e4nsch, E., Morin, P., Nochetto, R.H.: A finite element method for surface diffusion: the parametric case. J. Comput. Phys. 203(1), 321\u2013343 (2005)","journal-title":"J. Comput. Phys."},{"issue":"9","key":"1238_CR12","doi-asserted-by":"publisher","first-page":"3171","DOI":"10.1016\/j.jcp.2009.12.036","volume":"229","author":"A Bonito","year":"2010","unstructured":"Bonito, A., Nochetto, R.H., Pauletti, M.S.: Parametric FEM for geometric biomembranes. J. Comput. Phys. 229(9), 3171\u20133188 (2010)","journal-title":"J. Comput. Phys."},{"key":"1238_CR13","doi-asserted-by":"crossref","unstructured":"Bao, W., Zhao, Q.: A structure-preserving parametric finite element method for surface diffusion. arXiv:2104.01432 (2021)","DOI":"10.1137\/21M1406751"},{"issue":"3","key":"1238_CR14","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1017\/S0956792500002369","volume":"7","author":"JW Cahn","year":"1996","unstructured":"Cahn, J.W., Elliott, C.M., Novick-Cohen, A.: The Cahn\u2013Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature. Eur. J. Appl. Math. 7(3), 287\u2013301 (1996)","journal-title":"Eur. J. Appl. Math."},{"key":"1238_CR15","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1016\/j.jcp.2018.03.024","volume":"365","author":"Y Chen","year":"2018","unstructured":"Chen, Y., Lowengrub, J., Shen, J., Wang, C., Wise, S.: Efficient energy stable schemes for isotropic and strongly anisotropic Cahn\u2013Hilliard systems with the Willmore regularization. J. Comput. Phys. 365, 56\u201373 (2018)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"1238_CR16","doi-asserted-by":"publisher","first-page":"21","DOI":"10.4171\/IFB\/134","volume":"8","author":"K Deckelnick","year":"2006","unstructured":"Deckelnick, K., Dziuk, G.: Error analysis of a finite element method for the Willmore flow of graphs. Interfaces Free Bound. 8(1), 21\u201346 (2006)","journal-title":"Interfaces Free Bound."},{"issue":"266","key":"1238_CR17","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1090\/S0025-5718-08-02176-5","volume":"78","author":"K Deckelnick","year":"2009","unstructured":"Deckelnick, K., Dziuk, G.: Error analysis for the elastic flow of parametrized curves. Math. Comput. 78(266), 645\u2013671 (2009)","journal-title":"Math. Comput."},{"issue":"6","key":"1238_CR18","doi-asserted-by":"publisher","first-page":"2161","DOI":"10.1137\/S0036142902405382","volume":"41","author":"K Deckelnick","year":"2003","unstructured":"Deckelnick, K., Dziuk, G., Elliott, C.M.: Error analysis of a semidiscrete numerical scheme for diffusion in axially symmetric surfaces. SIAM J. Numer. Anal. 41(6), 2161\u20132179 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"1238_CR19","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1017\/S0962492904000224","volume":"14","author":"K Deckelnick","year":"2005","unstructured":"Deckelnick, K., Dziuk, G., Elliott, C.M.: Computation of geometric partial differential equations and mean curvature flow. Acta Numer. 14, 139\u2013232 (2005)","journal-title":"Acta Numer."},{"issue":"3","key":"1238_CR20","doi-asserted-by":"publisher","first-page":"1112","DOI":"10.1137\/S0036142903434874","volume":"43","author":"K Deckelnick","year":"2005","unstructured":"Deckelnick, K., Dziuk, G., Elliott, C.M.: Fully discrete finite element approximation for anisotropic surface diffusion of graphs. SIAM J. Numer. Anal. 43(3), 1112\u20131138 (2005)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"1238_CR21","doi-asserted-by":"publisher","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."},{"key":"1238_CR22","doi-asserted-by":"publisher","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":"281","key":"1238_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0025-5718-2012-02601-9","volume":"82","author":"G Dziuk","year":"2013","unstructured":"Dziuk, G., Elliott, C.M.: $$L^2$$-Estimates for the evolving surface finite element method. Math. Comput. 82(281), 1\u201324 (2013)","journal-title":"Math. Comput."},{"issue":"2","key":"1238_CR24","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1137\/070708135","volume":"47","author":"A Demlow","year":"2009","unstructured":"Demlow, A.: Higher-order finite element methods and pointwise error estimates for elliptic problems on surfaces. SIAM J. Numer. Anal. 47(2), 805\u2013807 (2009)","journal-title":"SIAM J. Numer. Anal."},{"issue":"296","key":"1238_CR25","doi-asserted-by":"publisher","first-page":"2617","DOI":"10.1090\/mcom\/2973","volume":"84","author":"K Deckelnick","year":"2015","unstructured":"Deckelnick, K., Katz, J., Schieweck, F.: A $$C^1$$-finite element method for the Willmore flow of two-dimensional graphs. Math. Comput. 84(296), 2617\u20132643 (2015)","journal-title":"Math. Comput."},{"issue":"2","key":"1238_CR26","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1093\/imanum\/drr017","volume":"32","author":"G Dziuk","year":"2012","unstructured":"Dziuk, G., Lubich, C., Mansour, D.E.: 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."},{"key":"1238_CR27","doi-asserted-by":"crossref","unstructured":"Dziuk, G.: Finite elements for the Beltrami operator on arbitrary surfaces. In: Partial Differential Equations and Calculus of Variations, Lecture Notes in Math., 1357, , pp. 142\u2013155. Springer, Berlin (1988)","DOI":"10.1007\/BFb0082865"},{"issue":"1","key":"1238_CR28","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/s00211-008-0179-1","volume":"111","author":"G Dziuk","year":"2008","unstructured":"Dziuk, G.: Computational parametric Willmore flow. Numer. Math. 111(1), 55\u201380 (2008)","journal-title":"Numer. Math."},{"key":"1238_CR29","volume-title":"Regularity Theory for Mean Curvature Flow","author":"K Ecker","year":"2012","unstructured":"Ecker, K.: Regularity Theory for Mean Curvature Flow. Birkh\u00e4user, Boston (2012)"},{"issue":"18","key":"1238_CR30","doi-asserted-by":"publisher","first-page":"6585","DOI":"10.1016\/j.jcp.2010.05.014","volume":"229","author":"CM Elliott","year":"2010","unstructured":"Elliott, C.M., Stinner, B.: Modeling and computation of two phase geometric biomembranes using surface finite elements. J. Comput. Phys. 229(18), 6585\u20136612 (2010)","journal-title":"J. Comput. Phys."},{"issue":"11\u201312","key":"1238_CR31","doi-asserted-by":"publisher","first-page":"693","DOI":"10.1515\/znc-1973-11-1209","volume":"28","author":"W Helfrich","year":"1973","unstructured":"Helfrich, W.: Elastic properties of lipid bilayers: theory and possible experiments. Zeitschrift f\u00fcr Naturforschung C 28(11\u201312), 693\u2013703 (1973)","journal-title":"Zeitschrift f\u00fcr Naturforschung C"},{"issue":"1","key":"1238_CR32","doi-asserted-by":"publisher","first-page":"237","DOI":"10.4310\/jdg\/1214438998","volume":"20","author":"G Huisken","year":"1984","unstructured":"Huisken, G.: Flow by mean curvature of convex surfaces into spheres. J. Differ. Geom. 20(1), 237\u2013266 (1984)","journal-title":"J. Differ. Geom."},{"key":"1238_CR33","doi-asserted-by":"crossref","unstructured":"Jiang, W., Li, B.: A perimeter-decreasing and area-conserving algorithm for surface diffusion flow of curves. arXiv:2102.00374 (2021)","DOI":"10.1016\/j.jcp.2021.110531"},{"issue":"4","key":"1238_CR34","doi-asserted-by":"publisher","first-page":"797","DOI":"10.1007\/s00211-019-01074-2","volume":"143","author":"B Kov\u00e1cs","year":"2019","unstructured":"Kov\u00e1cs, B., Li, B., Lubich, C.: A convergent evolving finite element algorithm for mean curvature flow of closed surfaces. Numer. Math. 143(4), 797\u2013853 (2019)","journal-title":"Numer. Math."},{"issue":"3","key":"1238_CR35","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1007\/s00211-017-0888-4","volume":"137","author":"B Kov\u00e1cs","year":"2017","unstructured":"Kov\u00e1cs, B., Li, B., Lubich, C., Power Guerra, C.A.: Convergence of finite elements on an evolving surface driven by diffusion on the surface. Numer. Math. 137(3), 643\u2013689 (2017)","journal-title":"Numer. Math."},{"issue":"1","key":"1238_CR36","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1093\/imanum\/drx013","volume":"38","author":"B Kov\u00e1cs","year":"2018","unstructured":"Kov\u00e1cs, B.: High-order evolving surface finite element method for parabolic problems on evolving surfaces. IMA J. Numer. Anal. 38(1), 430\u2013459 (2018)","journal-title":"IMA J. Numer. Anal."},{"issue":"3","key":"1238_CR37","doi-asserted-by":"publisher","first-page":"409","DOI":"10.4310\/jdg\/1090348128","volume":"57","author":"E Kuwert","year":"2001","unstructured":"Kuwert, E., Sch\u00e4tzle, R.: The Willmore flow with small initial energy. J. Differ. Geom. 57(3), 409\u2013441 (2001)","journal-title":"J. Differ. Geom."},{"issue":"2","key":"1238_CR38","doi-asserted-by":"publisher","first-page":"307","DOI":"10.4310\/CAG.2002.v10.n2.a4","volume":"10","author":"E Kuwert","year":"2002","unstructured":"Kuwert, E., Sch\u00e4tzle, R.: Gradient flow for the Willmore functional. Commun. Anal. Geom. 10(2), 307\u2013339 (2002)","journal-title":"Commun. Anal. Geom."},{"issue":"292","key":"1238_CR39","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1090\/S0025-5718-2014-02882-2","volume":"84","author":"C Lubich","year":"2015","unstructured":"Lubich, C., Mansour, D.E.: Variational discretization of wave equations on evolving surfaces. Math. Comput. 84(292), 513\u2013542 (2015)","journal-title":"Math. Comput."},{"key":"1238_CR40","doi-asserted-by":"crossref","unstructured":"Mantegazza, C.: Lecture Notes on Mean Curvature Flow. Progress in Mathematics, Vol. 290. Birkh\u00e4user, Corrected Printing (2012)","DOI":"10.1007\/978-3-0348-0145-4"},{"issue":"2","key":"1238_CR41","doi-asserted-by":"publisher","first-page":"683","DOI":"10.4007\/annals.2014.179.2.6","volume":"179","author":"FC Marques","year":"2014","unstructured":"Marques, F.C., Neves, A.: Min-Max theory and the Willmore conjecture. Ann. Math. 179(2), 683\u2013782 (2014)","journal-title":"Ann. Math."},{"key":"1238_CR42","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1063\/1.1722742","volume":"28","author":"WW Mullins","year":"1957","unstructured":"Mullins, W.W.: Theory of thermal grooving. J. Appl. Phys. 28, 333\u2013339 (1957)","journal-title":"J. Appl. Phys."},{"issue":"2","key":"1238_CR43","doi-asserted-by":"publisher","first-page":"189","DOI":"10.4171\/IFB\/339","volume":"17","author":"P Pozzi","year":"2015","unstructured":"Pozzi, P.: Computational anisotropic Willmore flow. Interfaces Free Bound. 17(2), 189\u2013232 (2015)","journal-title":"Interfaces Free Bound."},{"issue":"2","key":"1238_CR44","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1137\/S0036144503429121","volume":"46","author":"P-O 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."},{"issue":"1","key":"1238_CR45","first-page":"201","volume":"39","author":"P Pozzi","year":"2018","unstructured":"Pozzi, P., Stinner, B.: Elastic flow interacting with a lateral diffusion process: the one-dimensional graph case. IMA J. Numer. Anal. 39(1), 201\u2013234, 03 (2018)","journal-title":"IMA J. Numer. Anal."},{"issue":"3","key":"1238_CR46","doi-asserted-by":"publisher","first-page":"229","DOI":"10.4171\/IFB\/122","volume":"7","author":"RE Rusu","year":"2005","unstructured":"Rusu, R.E.: An algorithm for the elastic flow of surfaces. Interfaces Free Bound. 7(3), 229\u2013239 (2005)","journal-title":"Interfaces Free Bound."},{"issue":"1","key":"1238_CR47","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/BF02954615","volume":"3","author":"G Thomsen","year":"1924","unstructured":"Thomsen, G.: Grundlagen der konformen Fl\u00e4chentheorie. Abh. Math. Seminar Univ. Hamburg 3(1), 31\u201356 (1924)","journal-title":"Abh. Math. Seminar Univ. Hamburg"},{"key":"1238_CR48","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611973969","volume-title":"The Shape of Things: A Practical Guide to Differential Geometry and the Shape Derivative","author":"SW Walker","year":"2015","unstructured":"Walker, S.W.: The Shape of Things: A Practical Guide to Differential Geometry and the Shape Derivative. SIAM, Philadelphia (2015)"},{"key":"1238_CR49","unstructured":"Willmore, T.J.: Note on embedded surfaces. An. Sti. Univ. \u201cAl. I. Cuza\u201d Iasi Sect. I a Mat.(NS) B 11, 493\u2013496 (1965)"},{"key":"1238_CR50","series-title":"Oxford Science Publications","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198532538.001.0001","volume-title":"Riemannian Geometry","author":"TJ Willmore","year":"1993","unstructured":"Willmore, T.J.: Riemannian Geometry. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1993)"},{"issue":"1","key":"1238_CR51","doi-asserted-by":"publisher","first-page":"B327","DOI":"10.1137\/19M1281666","volume":"42","author":"Q Zhao","year":"2020","unstructured":"Zhao, Q., Jiang, W., Bao, W.: A parametric finite element method for solid-state dewetting problems in three dimensions. SIAM J. Sci. Comput. 42(1), B327\u2013B352 (2020)","journal-title":"SIAM J. Sci. Comput."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/link.springer.com\/content\/pdf\/10.1007\/s00211-021-01238-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/link.springer.com\/article\/10.1007\/s00211-021-01238-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/link.springer.com\/content\/pdf\/10.1007\/s00211-021-01238-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T08:54:15Z","timestamp":1699779255000},"score":1,"resource":{"primary":{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/link.springer.com\/10.1007\/s00211-021-01238-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11]]},"references-count":51,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["1238"],"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1007\/s00211-021-01238-z","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11]]},"assertion":[{"value":"29 July 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 August 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 October 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 November 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}