{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T10:33:28Z","timestamp":1749033208005,"version":"3.37.3"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,5,11]],"date-time":"2024-05-11T00:00:00Z","timestamp":1715385600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,11]],"date-time":"2024-05-11T00:00:00Z","timestamp":1715385600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071101","12171122"],"award-info":[{"award-number":["12071101","12171122"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shenzhen Science and Technology Program","award":["RCJC20210609103755110"],"award-info":[{"award-number":["RCJC20210609103755110"]}]},{"name":"Fundamental Research Project of Shenzhen","award":["JCYJ20190806143201649"],"award-info":[{"award-number":["JCYJ20190806143201649"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2022FRFK060026"],"award-info":[{"award-number":["2022FRFK060026"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s10915-024-02556-8","type":"journal-article","created":{"date-parts":[[2024,5,11]],"date-time":"2024-05-11T05:01:57Z","timestamp":1715403717000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Isoparametric Finite Element Method for Time-fractional Parabolic Equation on 2D Curved Domain"],"prefix":"10.1007","volume":"99","author":[{"given":"Zhixin","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0570-0124","authenticated-orcid":false,"given":"Minghui","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Liang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,11]]},"reference":[{"key":"2556_CR1","volume-title":"An introduction to the fractional calculus and fractional differential equations","author":"KS Miller","year":"1993","unstructured":"Miller, K.S., Ross, B.: An introduction to the fractional calculus and fractional differential equations. Wiley, New York (1993)"},{"key":"2556_CR2","volume-title":"Application of fractional calculus in physics","author":"R Hilfer","year":"2001","unstructured":"Hilfer, R.: Application of fractional calculus in physics. World Scientific, New Jersey (2001)"},{"key":"2556_CR3","volume-title":"Numerical methods of fractional partial differential equations and applications","author":"F Liu","year":"2015","unstructured":"Liu, F., Zhuang, P., Liu, Q.: Numerical methods of fractional partial differential equations and applications. Science Press, Beijing (2015)"},{"key":"2556_CR4","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/BF02832308","volume":"24","author":"S Momani","year":"2007","unstructured":"Momani, S., Odibat, Z.M.: Fractional green function for linear time-fractional inhomogeneous partial differential equations in fluid mechanics. J. Comput. Appl. Math. 24, 167\u201378 (2007)","journal-title":"J. Comput. Appl. Math."},{"key":"2556_CR5","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.jcp.2013.11.017","volume":"259","author":"GH Gao","year":"2014","unstructured":"Gao, G.H., Sun, Z.Z., Zhang, H.W.: A new fractional numerical differential formula to approximate the Caputo fractional derivative and its applications. J. Comput. Phys. 259, 33\u201350 (2014)","journal-title":"J. Comput. Phys."},{"key":"2556_CR6","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.apnum.2005.03.003","volume":"56","author":"ZZ Sun","year":"2006","unstructured":"Sun, Z.Z., Wu, X.: A fully discrete scheme for a diffusion wave system. Appl. Numer. Math. 56, 193\u2013209 (2006)","journal-title":"Appl. Numer. Math."},{"issue":"3","key":"2556_CR7","doi-asserted-by":"crossref","first-page":"2108","DOI":"10.1137\/080718942","volume":"47","author":"XJ Li","year":"2009","unstructured":"Li, X.J., Xu, C.J.: A space-time spectral method for the time fractional diffusion equation. SIAM J. Numer. Anal. 47(3), 2108\u20132131 (2009)","journal-title":"SIAM J. Numer. Anal."},{"key":"2556_CR8","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1016\/j.jcp.2007.02.001","volume":"225","author":"YM Lin","year":"2007","unstructured":"Lin, Y.M., Xu, C.J.: Finite difference\/spectral approximation for the time-fractional diffusion equation. J. Comput. Phys. 225, 1533\u20131552 (2007)","journal-title":"J. Comput. Phys."},{"key":"2556_CR9","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.apnum.2018.08.006","volume":"135","author":"CB Huang","year":"2019","unstructured":"Huang, C.B., Stynes, M.: A direct discontinuous Galerkin method for a time-fractional diffusion equation with a Robin boundary condition. Appl. Numer. Math. 135, 15\u201329 (2019)","journal-title":"Appl. Numer. Math."},{"key":"2556_CR10","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.apnum.2019.12.023","volume":"151","author":"M Li","year":"2020","unstructured":"Li, M., Shi, D.Y., Pei, L.F.: Convergence and superconvergence analysis of finite element methods for the time fractional diffusion equation. Appl. Numer. Math. 151, 141\u2013160 (2020)","journal-title":"Appl. Numer. Math."},{"key":"2556_CR11","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2019.112435","volume":"367","author":"CB Huang","year":"2020","unstructured":"Huang, C.B., Stynes, M.: Optimal spatial $$H^{1}$$-norm analysis of a finite element method for a time-fractional diffusion equation. J. Comput. Appl. Math. 367, 112435 (2020)","journal-title":"J. Comput. Appl. Math."},{"key":"2556_CR12","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/s10915-015-0152-y","volume":"70","author":"YM Zhao","year":"2017","unstructured":"Zhao, Y.M., Chen, P., Bu, W.P., Liu, X.T., Tang, Y.F.: Two mixed finite element methods for time-fractional diffusion equations. J. Sci. Comput. 70, 407\u2013428 (2017)","journal-title":"J. Sci. Comput."},{"key":"2556_CR13","first-page":"945","volume":"37","author":"S Karra","year":"2017","unstructured":"Karra, S., Mustapha, K., Pani, K.: Finite volume element method for two-dimensional fractional subdiffusion problems. IMA J. Numer. Anal. 37, 945\u2013964 (2017)","journal-title":"IMA J. Numer. Anal."},{"key":"2556_CR14","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.jcp.2018.08.033","volume":"375","author":"T Zhang","year":"2018","unstructured":"Zhang, T., Guo, Q.X.: The finite difference\/finite volume method for solving the fractional diffusion equation. J. Comput. Phys. 375, 120\u2013134 (2018)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"2556_CR15","first-page":"691","volume":"33","author":"B Jin","year":"2016","unstructured":"Jin, B., Lazarov, R., Zhou, Z.: An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data. IMA J. Numer. Anal. 33(1), 691\u2013698 (2016)","journal-title":"IMA J. Numer. Anal."},{"key":"2556_CR16","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1016\/j.jcp.2014.09.031","volume":"280","author":"AA Alikhanov","year":"2015","unstructured":"Alikhanov, A.A.: A new difference scheme for the time fractional diffusion equation. J. Comput. Phys. 280, 424\u2013438 (2015)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"2556_CR17","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1137\/16M1082329","volume":"55","author":"M Stynes","year":"2017","unstructured":"Stynes, M., O\u2019Riordan, E., Gracia, J.L.: Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation. SIAM J. Numer. Anal. 55(2), 1057\u20131079 (2017)","journal-title":"SIAM J. Numer. Anal."},{"key":"2556_CR18","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1007\/s10915-018-0863-y","volume":"79","author":"H Chen","year":"2019","unstructured":"Chen, H., Stynes, M.: Error analysis of a second-order method on fitted meshes for a time-fractional diffusion problem. J. Sci. Comput. 79, 624\u2013647 (2019)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"2556_CR19","doi-asserted-by":"crossref","first-page":"1112","DOI":"10.1137\/17M1131829","volume":"56","author":"HL Liao","year":"2018","unstructured":"Liao, H.L., Li, D.F., Zhang, J.W.: Sharp error estimate of the nonuniform L1 formula for linear reaction-subdiffusion equations. SIAM J. Numer. Anal. 56(2), 1112\u20131133 (2018)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"2556_CR20","doi-asserted-by":"crossref","first-page":"567","DOI":"10.4208\/cicp.OA-2020-0124","volume":"30","author":"HL Liao","year":"2021","unstructured":"Liao, H.L., McLean, W., Zhang, J.W.: A second-order scheme with nonuniform time steps for a linear reaction-subdiffusion problem. Commun. Comput. Phys. 30(2), 567\u2013601 (2021)","journal-title":"Commun. Comput. Phys."},{"key":"2556_CR21","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.cma.2018.12.011","volume":"346","author":"BT Jin","year":"2019","unstructured":"Jin, B.T., Lazarov, R., Zhou, Z.Z.: Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview. Comput. Meth. Appl. Mech. Engin. 346, 332\u2013358 (2019)","journal-title":"Comput. Meth. Appl. Mech. Engin."},{"issue":"319","key":"2556_CR22","doi-asserted-by":"crossref","first-page":"2135","DOI":"10.1090\/mcom\/3410","volume":"88","author":"N Kopteva","year":"2019","unstructured":"Kopteva, N.: Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions. Math. Comput. 88(319), 2135\u20132155 (2019)","journal-title":"Math. Comput."},{"key":"2556_CR23","doi-asserted-by":"crossref","first-page":"1823","DOI":"10.1007\/s10915-019-01064-4","volume":"81","author":"M Li","year":"2019","unstructured":"Li, M., Zhao, J.K., Huang, C.M., Chen, S.C.: Nonconforming virtual element method for the time fractional reaction-subdiffusion equation with non-smooth data. J. Sci. Comput. 81, 1823\u20131859 (2019)","journal-title":"J. Sci. Comput."},{"key":"2556_CR24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.camwa.2022.01.033","volume":"110","author":"YD Zhang","year":"2022","unstructured":"Zhang, Y.D., Feng, M.F.: The virtual element method for the time fractional convection diffusion reaction equation with non-smooth data. Comput. Math. Appl. 110, 1\u201318 (2022)","journal-title":"Comput. Math. Appl."},{"key":"2556_CR25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.apnum.2021.05.021","volume":"168","author":"S Toprakseven","year":"2021","unstructured":"Toprakseven, S.: A weak Galerkin finite element method for time fractional reaction-diffusion-convection problems with variable coefficients. Appl. Numer. Math. 168, 1\u201312 (2021)","journal-title":"Appl. Numer. Math."},{"key":"2556_CR26","volume":"386","author":"XP Wang","year":"2020","unstructured":"Wang, X.P., Gao, F.Z., Liu, Y., Sun, Z.J.: A weak Galerkin finite element method for high dimensional time-fractional diffusion equation. Appl. Math. Comput. 386, 125524 (2020)","journal-title":"Appl. Math. Comput."},{"key":"2556_CR27","doi-asserted-by":"crossref","first-page":"3285","DOI":"10.1016\/j.cam.2011.01.011","volume":"235","author":"Y Jiang","year":"2011","unstructured":"Jiang, Y., Ma, J.: High-order finite element methods for time-fractional partial differential equations. J. Comput. Appl. Math. 235, 3285\u20133290 (2011)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"2556_CR28","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1007\/s10543-018-0707-z","volume":"58","author":"CB Huang","year":"2018","unstructured":"Huang, C.B., Stynes, M., An, N.: Optimal $$L^{\\infty }(L^{2})$$ error analysis of a direct discontinuous Galerkin method for a time-fractional reaction-diffusion problem. BIT Numer. Math. 58(3), 661\u2013690 (2018)","journal-title":"BIT Numer. Math."},{"key":"2556_CR29","doi-asserted-by":"crossref","first-page":"1334","DOI":"10.1016\/j.camwa.2019.05.031","volume":"78","author":"MRS Ammi","year":"2019","unstructured":"Ammi, M.R.S., Jamiai, I., Torres, D.F.M.: A finite element approximation for a class of Caputo time-fractional diffusion equations. Comput. Math. Appl. 78, 1334\u20131344 (2019)","journal-title":"Comput. Math. Appl."},{"key":"2556_CR30","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1016\/j.jcp.2014.10.051","volume":"281","author":"BT Jin","year":"2015","unstructured":"Jin, B.T., Lazarov, R., Liu, Y.K., Zhou, Z.: The Galerkin finite element method for a multi-term time-fractional diffusion equation. J. Comput. Phys. 281, 825\u2013843 (2015)","journal-title":"J. Comput. Phys."},{"key":"2556_CR31","doi-asserted-by":"crossref","first-page":"2309","DOI":"10.1007\/s40314-017-0447-8","volume":"37","author":"M Li","year":"2018","unstructured":"Li, M., Huang, C.M., Ming, W.Y.: Mixed finite-element method for multi-term time-fractional diffusion and diffusion-wave equations. Comp. Appl. Math. 37, 2309\u20132334 (2018)","journal-title":"Comp. Appl. Math."},{"key":"2556_CR32","volume-title":"The finite element method for elliptic problems","author":"PG Ciarlet","year":"1978","unstructured":"Ciarlet, P.G.: The finite element method for elliptic problems. North-Holland, Amsterdam (1978)"},{"key":"2556_CR33","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/0045-7825(72)90006-0","volume":"1","author":"PG Ciarlet","year":"1972","unstructured":"Ciarlet, P.G., Raviart, P.A.: Interpolation theory over curved elements with applications to finite element methods. Comput. Meth. Appl. Mech. Engin. 1, 217\u2013249 (1972)","journal-title":"Comput. Meth. Appl. Mech. Engin."},{"key":"2556_CR34","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1137\/0710022","volume":"10","author":"M Zl\u00e1mal","year":"1973","unstructured":"Zl\u00e1mal, M.: Curved elements in the finite element method. SIAM J. Numer. Anal. 10, 229\u2013240 (1973)","journal-title":"SIAM J. Numer. Anal."},{"key":"2556_CR35","doi-asserted-by":"crossref","first-page":"1756","DOI":"10.1016\/j.camwa.2018.05.029","volume":"77","author":"V Ruas","year":"2019","unstructured":"Ruas, V.: Accuracy enhancement for non-isoparametric finite-element simulations in curved domains application to fluid flow. Comput. Math. Appl. 77, 1756\u20131769 (2019)","journal-title":"Comput. Math. Appl."},{"key":"2556_CR36","volume":"381","author":"L Mu","year":"2021","unstructured":"Mu, L.: Weak Galerkin finite element with curved edges. J. Comput. Appl. Math. 381, 113038 (2021)","journal-title":"J. Comput. Appl. Math."},{"key":"2556_CR37","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1051\/m2an\/2018052","volume":"53","author":"LBD Veiga","year":"2019","unstructured":"Veiga, L.B.D., Russo, A., Vacca, G.: The virtual element method with curved edges. ESAIM Math. odel. Numer. Anal. 53, 375\u2013404 (2019)","journal-title":"ESAIM Math. odel. Numer. Anal."},{"key":"2556_CR38","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1137\/0723036","volume":"23","author":"M Lenoir","year":"1986","unstructured":"Lenoir, M.: Optimal isoparametric finite elements and error estimates for domains involving curved boundaries. SIAM J. Numer. Anal. 23, 562\u2013580 (1986)","journal-title":"SIAM J. Numer. Anal."},{"key":"2556_CR39","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1002\/num.22595","volume":"37","author":"SC Song","year":"2021","unstructured":"Song, S.C., Liu, Z.X.: A second-order isoparametric element method to solve plane linear elastic problem. Numer. Meth. Part. Diff. Eq. 37, 1535\u20131550 (2021)","journal-title":"Numer. Meth. Part. Diff. Eq."},{"key":"2556_CR40","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2021.113523","volume":"394","author":"V Ruas","year":"2021","unstructured":"Ruas, V., Ramos, M.A.S.: Efficiency of nonparametric finite elements for optimal-order enforcement of Dirichlet conditions on curvilinear boundaries. J. Comput. Appl. Math. 394, 113523 (2021)","journal-title":"J. Comput. Appl. Math."},{"issue":"4","key":"2556_CR41","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.4208\/cicp.OA-2022-0106","volume":"32","author":"Y Liu","year":"2022","unstructured":"Liu, Y., Chen, W.B., Wang, Y.Q.: A weak Galerkin mixed finite element method for second order elliptic equation on 2D cueved domains. Commun. Comput. Phys. 32(4), 1094\u20131128 (2022)","journal-title":"Commun. Comput. Phys."},{"key":"2556_CR42","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1007\/s10915-021-01683-w","volume":"90","author":"D Franco","year":"2022","unstructured":"Franco, D., Alessio, F., Ilario, M., Anna, S., Giuseppe, V.: A virtual element method for the wave equation on curved edges in two dimensions. J. Sci. Comput. 90, 50 (2022)","journal-title":"J. Sci. Comput."},{"key":"2556_CR43","doi-asserted-by":"crossref","first-page":"408","DOI":"10.21136\/AM.1978.103769","volume":"23","author":"J Nedoma","year":"1978","unstructured":"Nedoma, J.: The finite element solution of parabolic equations. Appl. Math. 23, 408\u2013438 (1978)","journal-title":"Appl. Math."},{"key":"2556_CR44","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1051\/m2an\/1979130302571","volume":"13","author":"J Nedoma","year":"1979","unstructured":"Nedoma, J.: The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements. RAIRO. Anal. Numer. 13, 257\u2013289 (1979)","journal-title":"RAIRO. Anal. Numer."},{"key":"2556_CR45","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.camwa.2021.05.017","volume":"96","author":"ZX Liu","year":"2021","unstructured":"Liu, Z.X., Song, S.C.: An isoparametric mixed finite element method for approximating a class of fourth-order elliptic problem. Comput. Math. Appl. 96, 77\u201394 (2021)","journal-title":"Comput. Math. Appl."},{"key":"2556_CR46","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1051\/m2an:2002001","volume":"36","author":"PK Bhattacharyya","year":"2002","unstructured":"Bhattacharyya, P.K., Nataraj, N.: Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4-th order eigenvalue problems with variable coefficients. ESAIM Math. Model. Numer. Anal. 36, 1\u201332 (2002)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"2556_CR47","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1051\/m2an\/1993270505651","volume":"27","author":"M Vanmaele","year":"1993","unstructured":"Vanmaele, M., \u017de\u0144\u0131\u0161ek, A.: External finite-element approximations of eigenvalue problems. Math. Model. Num. Anal. 27, 565\u2013589 (1993)","journal-title":"Math. Model. Num. Anal."},{"issue":"1","key":"2556_CR48","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1137\/16M1175742","volume":"57","author":"HL Liao","year":"2019","unstructured":"Liao, H.L., McLean, W., Zhang, J.W.: A discrete Gr\u00f6nwall inequality with applications to numerical schemes for subdiffusion problems. SIAM J. Numer. Anal. 57(1), 218\u2013237 (2019)","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-024-02556-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-024-02556-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-024-02556-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,23]],"date-time":"2024-05-23T14:21:45Z","timestamp":1716474105000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-024-02556-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,11]]},"references-count":48,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["2556"],"URL":"https:\/\/doi.org\/10.1007\/s10915-024-02556-8","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2024,5,11]]},"assertion":[{"value":"7 April 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 April 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 May 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"88"}}