{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T11:18:04Z","timestamp":1779275884448,"version":"3.51.4"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T00:00:00Z","timestamp":1660608000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T00:00:00Z","timestamp":1660608000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2022,9]]},"DOI":"10.1007\/s00211-022-01308-w","type":"journal-article","created":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T06:03:12Z","timestamp":1660629792000},"page":"67-99","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A DPG method for shallow shells"],"prefix":"10.1007","volume":"152","author":[{"given":"Thomas","family":"F\u00fchrer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Norbert","family":"Heuer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antti H.","family":"Niemi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,8,16]]},"reference":[{"key":"1308_CR1","doi-asserted-by":"publisher","first-page":"1311","DOI":"10.1002\/nme.1620360805","volume":"36","author":"U Andelfinger","year":"1993","unstructured":"Andelfinger, U., Ramm, E.: EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements. Internat. J. Numer. Methods Engrg. 36, 1311\u20131337 (1993)","journal-title":"Internat. J. Numer. Methods Engrg."},{"key":"1308_CR2","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/0045-7825(84)90152-X","volume":"45","author":"JW Barrett","year":"1984","unstructured":"Barrett, J.W., Morton, K.W.: Approximate symmetrization and Petrov-Galerkin methods for diffusion-convection problems. Comput. Methods Appl. Mech. Engrg. 45, 97\u2013122 (1984)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"1308_CR3","doi-asserted-by":"publisher","first-page":"1326","DOI":"10.1016\/j.cma.2009.08.023","volume":"199","author":"F B\u00e9chet","year":"2010","unstructured":"B\u00e9chet, F., Sanchez-Palencia, E., Millet, O.: Singularities in shell theory: anisotropic error estimates and numerical simulations. Comput. Methods Appl. Mech. Engrg. 199, 1326\u20131341 (2010)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"1308_CR4","doi-asserted-by":"publisher","first-page":"113544, 52","DOI":"10.1016\/j.cma.2020.113544","volume":"374","author":"J Benzaken","year":"2021","unstructured":"Benzaken, J., Evans, J.A., McCormick, S.F., Tamstorf, R.: Nitsche\u2019s method for linear Kirchhoff-Love shells: formulation, error analysis, and verification. Comput. Methods Appl. Mech. Engrg. 374, 113544, 52 (2021)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"1308_CR5","doi-asserted-by":"publisher","first-page":"3391","DOI":"10.1016\/S0045-7825(02)00254-2","volume":"191","author":"CL Bottasso","year":"2002","unstructured":"Bottasso, C.L., Micheletti, S., Sacco, R.: The discontinuous Petrov-Galerkin method for elliptic problems. Comput. Methods Appl. Mech. Engrg. 191, 3391\u20133409 (2002)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"1308_CR6","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1007\/s00211-012-0476-6","volume":"122","author":"J Bramwell","year":"2012","unstructured":"Bramwell, J., Demkowicz, L.F., Gopalakrishnan, J., Qiu, W.: A locking-free $$hp$$ DPG method for linear elasticity with symmetric stresses. Numer. Math. 122, 671\u2013707 (2012)","journal-title":"Numer. Math."},{"key":"1308_CR7","volume-title":"The Mathematical Theory of Finite Element Methods, no.\u00a015 in Texts in Applied Mathematics","author":"SC Brenner","year":"1994","unstructured":"Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods, no.\u00a015 in Texts in Applied Mathematics. Springer-Verlag, New York (1994)"},{"key":"1308_CR8","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1002\/nme.436","volume":"54","author":"D Briassoulis","year":"2002","unstructured":"Briassoulis, D.: Testing the asymptotic behaviour of shell elements-Part I: the classical benchmark tests. Internat. J. Numer. Methods Engrg. 54, 421\u2013452 (2002)","journal-title":"Internat. J. Numer. Methods Engrg."},{"key":"1308_CR9","doi-asserted-by":"publisher","first-page":"1335","DOI":"10.1137\/130924913","volume":"52","author":"C Carstensen","year":"2014","unstructured":"Carstensen, C., Demkowicz, L.F., Gopalakrishnan, J.: A posteriori error control for DPG methods. SIAM J. Numer. Anal. 52, 1335\u20131353 (2014)","journal-title":"SIAM J. Numer. Anal."},{"key":"1308_CR10","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1016\/j.camwa.2016.05.004","volume":"72","author":"C Carstensen","year":"2016","unstructured":"Carstensen, C., Demkowicz, L.F., Gopalakrishnan, J.: Breaking spaces and forms for the DPG method and applications including Maxwell equations. Comput. Math. Appl. 72, 494\u2013522 (2016)","journal-title":"Comput. Math. Appl."},{"key":"1308_CR11","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1137\/S0036142995285873","volume":"35","author":"O Cessenat","year":"1998","unstructured":"Cessenat, O., Despr\u00e9s, B.: Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem. SIAM J. Numer. Anal. 35, 255\u2013299 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"1308_CR12","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/S0045-7949(97)00078-3","volume":"66","author":"D Chapelle","year":"1998","unstructured":"Chapelle, D., Bathe, K.J.: Fundamental considerations for the finite element analysis of shell structures. Computers & Structures 66, 19\u201336 (1998)","journal-title":"Computers & Structures"},{"key":"1308_CR13","doi-asserted-by":"publisher","first-page":"1558","DOI":"10.1016\/j.cma.2010.01.003","volume":"199","author":"LF Demkowicz","year":"2010","unstructured":"Demkowicz, L.F., Gopalakrishnan, J.: A class of discontinuous Petrov-Galerkin methods. Part I: the transport equation. Comput. Methods Appl. Mech. Engrg. 199, 1558\u20131572 (2010)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"1308_CR14","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1002\/num.20640","volume":"27","author":"LF Demkowicz","year":"2011","unstructured":"Demkowicz, L.F., Gopalakrishnan, J.: A class of discontinuous Petrov-Galerkin methods. Part II: Optimal test functions. Numer. Methods Partial Differential Eq. 27, 70\u2013105 (2011)","journal-title":"Numer. Methods Partial Differential Eq."},{"key":"1308_CR15","doi-asserted-by":"crossref","unstructured":"L.\u00a0F. Demkowicz and J.\u00a0Gopalakrishnan, An overview of the discontinuous Petrov Galerkin method, in Recent developments in discontinuous Galerkin finite element methods for partial differential equations, vol.\u00a0157 of IMA Vol. Math. Appl., Springer, Cham, 2014, pp.\u00a0149\u2013180","DOI":"10.1007\/978-3-319-01818-8_6"},{"key":"1308_CR16","doi-asserted-by":"publisher","first-page":"1740","DOI":"10.1137\/16M1099765","volume":"55","author":"LF Demkowicz","year":"2017","unstructured":"Demkowicz, L.F., Gopalakrishnan, J., Nagaraj, S., Sep\u00falveda, P.: A spacetime DPG method for the Schr\u00f6dinger equation. SIAM J. Numer. Anal. 55, 1740\u20131759 (2017)","journal-title":"SIAM J. Numer. Anal."},{"key":"1308_CR17","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1016\/j.apnum.2011.09.002","volume":"62","author":"LF Demkowicz","year":"2012","unstructured":"Demkowicz, L.F., Gopalakrishnan, J., Niemi, A.H.: A class of discontinuous Petrov-Galerkin methods. Part III: Adaptivity. Appl. Numer. Math. 62, 396\u2013427 (2012)","journal-title":"Appl. Numer. Math."},{"key":"1308_CR18","doi-asserted-by":"publisher","first-page":"2514","DOI":"10.1137\/120862065","volume":"51","author":"LF Demkowicz","year":"2013","unstructured":"Demkowicz, L.F., Heuer, N.: Robust DPG method for convection-dominated diffusion problems. SIAM J. Numer. Anal. 51, 2514\u20132537 (2013)","journal-title":"SIAM J. Numer. Anal."},{"key":"1308_CR19","first-page":"939","volume":"318","author":"B Despr\u00e9s","year":"1994","unstructured":"Despr\u00e9s, B.: Sur une formulation variationnelle de type ultra-faible. C. R. Acad. Sci. Paris S\u00e9r. I Math. 318, 939\u2013944 (1994)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"key":"1308_CR20","unstructured":"W.\u00a0Fl\u00fcgge, Stresses in Shells, Springer-Verlag, Berlin-G\u00f6ttingen-Heidelberg, 1960. Translation of Statik und Dynamik der Schalen, Springer, 1934"},{"key":"1308_CR21","doi-asserted-by":"publisher","first-page":"1705","DOI":"10.1016\/j.camwa.2017.11.029","volume":"75","author":"T F\u00fchrer","year":"2018","unstructured":"F\u00fchrer, T.: Superconvergence in a DPG method for an ultra-weak formulation. Comput. Math. Appl. 75, 1705\u20131718 (2018)","journal-title":"Comput. Math. Appl."},{"key":"1308_CR22","first-page":"483","volume":"19","author":"T F\u00fchrer","year":"2019","unstructured":"F\u00fchrer, T.: Superconvergent DPG methods for second-order elliptic problems, Comput. Methods. Appl. Math. 19, 483\u2013502 (2019)","journal-title":"Appl. Math."},{"key":"1308_CR23","doi-asserted-by":"publisher","first-page":"1031","DOI":"10.1093\/imanum\/draa012","volume":"41","author":"T F\u00fchrer","year":"2021","unstructured":"F\u00fchrer, T., Haberl, A., Heuer, N.: Trace operators of the bi-Laplacian and applications. IMA J. Numer. Anal. 41, 1031\u20131055 (2021)","journal-title":"IMA J. Numer. Anal."},{"key":"1308_CR24","doi-asserted-by":"publisher","first-page":"550","DOI":"10.1016\/j.cma.2018.08.041","volume":"343","author":"T F\u00fchrer","year":"2019","unstructured":"F\u00fchrer, T., Heuer, N.: Fully discrete DPG methods for the Kirchhoff-Love plate bending model. Comput. Methods Appl. Mech. Engrg. 343, 550\u2013571 (2019)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"1308_CR25","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/j.camwa.2021.04.021","volume":"94","author":"T F\u00fchrer","year":"2021","unstructured":"F\u00fchrer, T., Heuer, N.: A robust DPG method for large domains. Comput. Math. Appl. 94, 15\u201327 (2021)","journal-title":"Comput. Math. Appl."},{"key":"1308_CR26","doi-asserted-by":"publisher","first-page":"1587","DOI":"10.1090\/mcom\/3381","volume":"88","author":"T F\u00fchrer","year":"2019","unstructured":"F\u00fchrer, T., Heuer, N., Niemi, A.H.: An ultraweak formulation of the Kirchhoff-Love plate bending model and DPG approximation. Math. Comp. 88, 1587\u20131619 (2019)","journal-title":"Math. Comp."},{"key":"1308_CR27","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/s00211-020-01116-0","volume":"145","author":"T F\u00fchrer","year":"2020","unstructured":"F\u00fchrer, T., Heuer, N., Sayas, F.-J.: An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation. Numer. Math. 145, 313\u2013344 (2020)","journal-title":"Numer. Math."},{"key":"1308_CR28","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1090\/S0025-5718-2013-02721-4","volume":"83","author":"J Gopalakrishnan","year":"2014","unstructured":"Gopalakrishnan, J., Qiu, W.: An analysis of the practical DPG method. Math. Comp. 83, 537\u2013552 (2014)","journal-title":"Math. Comp."},{"key":"1308_CR29","doi-asserted-by":"publisher","first-page":"1218","DOI":"10.1137\/15M1041304","volume":"55","author":"N Heuer","year":"2017","unstructured":"Heuer, N., Karkulik, M.: A robust DPG method for singularly perturbed reaction-diffusion problems. SIAM J. Numer. Anal. 55, 1218\u20131242 (2017)","journal-title":"SIAM J. Numer. Anal."},{"key":"1308_CR30","unstructured":"MacNeal, R.H.: Finite Elements: Their Design and Performance. Marcel Dekker, Inc. (1994)"},{"key":"1308_CR31","doi-asserted-by":"crossref","unstructured":"Malinen, M.: On the classical shell model underlying bilinear degenerated shell finite elements. Internat. J. Numer. Methods Engrg. 52, 389\u2013416 (2001)","DOI":"10.1002\/nme.216"},{"key":"1308_CR32","doi-asserted-by":"publisher","first-page":"1783","DOI":"10.1051\/m2an\/2017009","volume":"51","author":"I Merabet","year":"2017","unstructured":"Merabet, I., Nicaise, S.: A penalty method for a linear Koiter shell model. ESAIM Math. Model. Numer. Anal. 51, 1783\u20131803 (2017)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"1308_CR33","doi-asserted-by":"publisher","first-page":"3964","DOI":"10.1016\/j.cma.2008.03.021","volume":"197","author":"AH Niemi","year":"2008","unstructured":"Niemi, A.H.: Approximation of shell layers using bilinear elements on anisotropically refined rectangular meshes. Comput. Methods Appl. Mech. Engrg. 197, 3964\u20133975 (2008)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"1308_CR34","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1002\/nme.2701","volume":"81","author":"AH Niemi","year":"2010","unstructured":"Niemi, A.H.: A bilinear shell element based on a refined shallow shell model. Internat. J. Numer. Methods Engrg. 81, 485\u2013512 (2010)","journal-title":"Internat. J. Numer. Methods Engrg."},{"key":"1308_CR35","doi-asserted-by":"publisher","first-page":"B440","DOI":"10.1137\/15M1027590","volume":"38","author":"AH Niemi","year":"2016","unstructured":"Niemi, A.H.: Benchmark computations of stresses in a spherical dome with shell finite elements. SIAM J. Sci. Comput. 38, B440\u2013B457 (2016)","journal-title":"SIAM J. Sci. Comput."},{"key":"1308_CR36","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1007\/978-3-540-69777-0_98","volume-title":"Numerical Mathematics and Advanced Applications","author":"AH Niemi","year":"2008","unstructured":"Niemi, A.H., Hakula, H., Pitk\u00e4ranta, J.: Point load on a shell. In: Kunisch, K., Of, G., Steinbach, O. (eds.) Numerical Mathematics and Advanced Applications, pp. 819\u2013826. Springer, Berlin, Heidelberg (2008)"},{"key":"1308_CR37","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1016\/j.cma.2006.07.012","volume":"196","author":"AH Niemi","year":"2007","unstructured":"Niemi, A.H., Pitk\u00e4ranta, J., Hakula, H.: Benchmark computations on point-loaded shallow shells: Fourier vs. FEM. Comput. Methods Appl. Mech. Engrg. 196, 894\u2013907 (2007)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"1308_CR38","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1142\/S0218202594000108","volume":"4","author":"J Piila","year":"1994","unstructured":"Piila, J.: Characterization of the membrane theory of a clamped shell. The elliptic case, Math. Models Methods Appl. Sci. 4, 147\u2013177 (1994)","journal-title":"The elliptic case, Math. Models Methods Appl. Sci."},{"key":"1308_CR39","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1142\/S0218202596000535","volume":"6","author":"J Piila","year":"1996","unstructured":"Piila, J.: Characterization of the membrane theory of a clamped shell. The hyperbolic case, Math. Models Methods Appl. Sci. 6, 169\u2013194 (1996)","journal-title":"The hyperbolic case, Math. Models Methods Appl. Sci."},{"key":"1308_CR40","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1142\/S0218202593000229","volume":"3","author":"J Piila","year":"1993","unstructured":"Piila, J., Pitk\u00e4ranta, J.: Characterization of the membrane theory of a clamped shell. The parabolic case, Math. Models Methods Appl. Sci. 3, 417\u2013442 (1993)","journal-title":"The parabolic case, Math. Models Methods Appl. Sci."},{"key":"1308_CR41","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/0524001","volume":"24","author":"J Piila","year":"1993","unstructured":"Piila, J., Pitk\u00e4ranta, J.: Energy estimates relating different linear elastic models of a thin cylindrical shell. I. The membrane-dominated case. SIAM J. Math. Anal. 24, 1\u201322 (1993)","journal-title":"SIAM J. Math. Anal."},{"key":"1308_CR42","doi-asserted-by":"publisher","first-page":"820","DOI":"10.1137\/S0036141092198031","volume":"26","author":"J Piila","year":"1995","unstructured":"Piila, J., Pitk\u00e4ranta, J.: Energy estimates relating different linear elastic models of a thin cylindrical shell. II. The case of free boundary. SIAM J. Math. Anal. 26, 820\u2013849 (1995)","journal-title":"SIAM J. Math. Anal."},{"key":"1308_CR43","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1007\/BF01385524","volume":"61","author":"J Pitk\u00e4ranta","year":"1992","unstructured":"Pitk\u00e4ranta, J.: The problem of membrane locking in finite element analysis of cylindrical shells. Numer. Math. 61, 523\u2013542 (1992)","journal-title":"Numer. Math."},{"key":"1308_CR44","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/0045-7825(95)00870-X","volume":"128","author":"J Pitk\u00e4ranta","year":"1995","unstructured":"Pitk\u00e4ranta, J., Leino, Y., Ovaskainen, O., Piila, J.: Shell deformation states and the finite element method: a benchmark study of cylindrical shells. Comput. Methods Appl. Mech. Engrg. 128, 81\u2013121 (1995)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"1308_CR45","doi-asserted-by":"publisher","first-page":"2943","DOI":"10.1016\/S0045-7825(00)00276-0","volume":"190","author":"J Pitk\u00e4ranta","year":"2001","unstructured":"Pitk\u00e4ranta, J., Matache, A.-M., Schwab, C.: Fourier mode analysis of layers in shallow shell deformations. Comput. Methods Appl. Mech. Engrg. 190, 2943\u20132975 (2001)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"1308_CR46","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1016\/j.cma.2018.11.033","volume":"346","author":"K Rafetseder","year":"2019","unstructured":"Rafetseder, K., Zulehner, W.: A new mixed approach to Kirchhoff-Love shells. Comput. Methods Appl. Mech. Engrg. 346, 440\u2013455 (2019)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"1308_CR47","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1002\/nme.967","volume":"60","author":"E Ramm","year":"2004","unstructured":"Ramm, E., Wall, W.A.: Shell structures\u2013a sensitive interrelation between physics and numerics. Internat. J. Numer. Methods Engrg. 60, 381\u2013427 (2004)","journal-title":"Internat. J. Numer. Methods Engrg."},{"key":"1308_CR48","first-page":"539","volume":"61","author":"AC Scordelis","year":"1964","unstructured":"Scordelis, A.C., Lo, K.S.: Computer analysis of cylindrical shells. J. Am. Concr. Inst. 61, 539\u2013561 (1964)","journal-title":"J. Am. Concr. Inst."},{"key":"1308_CR49","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s00211-015-0747-0","volume":"133","author":"S Zhang","year":"2016","unstructured":"Zhang, S.: Analysis of a discontinuous Galerkin method for the bending problem of Koiter shell. Numer. Math. 133, 333\u2013370 (2016)","journal-title":"Numer. Math."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-022-01308-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00211-022-01308-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-022-01308-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,27]],"date-time":"2022-08-27T16:03:30Z","timestamp":1661616210000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00211-022-01308-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,16]]},"references-count":49,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["1308"],"URL":"https:\/\/doi.org\/10.1007\/s00211-022-01308-w","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,16]]},"assertion":[{"value":"15 July 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 May 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 July 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 August 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}