{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:39:49Z","timestamp":1740123589112,"version":"3.37.3"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T00:00:00Z","timestamp":1713225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T00:00:00Z","timestamp":1713225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"NSFC General Project","award":["No.12171071"],"award-info":[{"award-number":["No.12171071"]}]},{"DOI":"10.13039\/501100018542","name":"Natural Science Foundation of Sichuan Province","doi-asserted-by":"publisher","award":["No.2023NSFSC0055"],"award-info":[{"award-number":["No.2023NSFSC0055"]}],"id":[{"id":"10.13039\/501100018542","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":[[2024,5]]},"DOI":"10.1007\/s10915-024-02522-4","type":"journal-article","created":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T15:28:39Z","timestamp":1713281319000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Analysis of an Energy-Dissipating Finite Volume Scheme on Admissible Mesh for the Aggregation-Diffusion Equations"],"prefix":"10.1007","volume":"99","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8712-1934","authenticated-orcid":false,"given":"Ping","family":"Zeng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanyu","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,4,16]]},"reference":[{"issue":"2","key":"2522_CR1","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1051\/m2an:1999118","volume":"33","author":"D Benedetto","year":"1999","unstructured":"Benedetto, D., Caglioti, E., Pulvirenti, M.: A kinetic equation for granular media. ESAIM: Math. Model. Numer. Anal. 33(2), 439\u2013441 (1999)","journal-title":"ESAIM: Math. Model. Numer. Anal."},{"issue":"1","key":"2522_CR2","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1137\/12087387X","volume":"4","author":"J Garnier","year":"2013","unstructured":"Garnier, J., Papanicolaou, G., Yang, T.W.: Large deviations for a mean field model of systemic risk. J. Financial Math. 4(1), 151\u2013184 (2013)","journal-title":"J. Financial Math."},{"issue":"2","key":"2522_CR3","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.physd.2006.07.010","volume":"220","author":"D Holm","year":"2006","unstructured":"Holm, D., Putkaradze, V.: Formation of clumps and patches in self-aggregation of finite-size particles. Physica D 220(2), 183\u2013196 (2006)","journal-title":"Physica D"},{"key":"2522_CR4","volume-title":"Sobolev spaces","author":"RA Adams","year":"2003","unstructured":"Adams, R.A., Fournier, J.J.: Sobolev spaces. Elsevier, Amsterdam (2003)"},{"issue":"1","key":"2522_CR5","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1051\/m2an\/1981150100031","volume":"15","author":"K Baba","year":"1981","unstructured":"Baba, K., Tabata, M.: On a conservation upwind finite element scheme for convective diffusion equations. RAIRO Anal. Num\u00e9r. 15(1), 3\u201325 (1981)","journal-title":"RAIRO Anal. Num\u00e9r."},{"issue":"5","key":"2522_CR6","first-page":"1259","volume":"18","author":"R Bailo","year":"2018","unstructured":"Bailo, R., Carrillo, J.A., Hu, J.: Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient flow structure. Math. Sci. 18(5), 1259\u20131303 (2018)","journal-title":"Math. Sci."},{"issue":"13","key":"2522_CR7","doi-asserted-by":"crossref","first-page":"2487","DOI":"10.1142\/S0218202520500487","volume":"30","author":"R Bailo","year":"2020","unstructured":"Bailo, R., Carrillo, J.A., Murakawa, H., Schmidtchen, M.: Convergence of a fully discrete and energy-dissipating finite-volume scheme for aggregation-diffusion equations. Math. Models Methods Appl. Sci. 30(13), 2487\u20132522 (2020)","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"3","key":"2522_CR8","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1137\/15M1043637","volume":"14","author":"ABT Barbaro","year":"2016","unstructured":"Barbaro, A.B.T., Canizo, J.A., Carrillo, J.A., Degond, P.: Phase transitions in a kinetic flocking model of Cucker-Smale type. Multiscale Model. Simul. 14(3), 1063\u20131088 (2016)","journal-title":"Multiscale Model. Simul."},{"key":"2522_CR9","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1023\/A:1023032000560","volume":"91","author":"D Benedetto","year":"1998","unstructured":"Benedetto, D., Caglioti, E., Carrillo, J.A., Pulvirenti, M.: A non-Maxwellian steady distribution for one-dimensional granular media. J. Stat. Phys. 91, 979\u2013990 (1998)","journal-title":"J. Stat. Phys."},{"issue":"5","key":"2522_CR10","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1051\/m2an\/1997310506151","volume":"31","author":"D Benedetto","year":"1997","unstructured":"Benedetto, D., Caglioti, E., Pulvirenti, M.: A kinetic equation for granular media. ESAIM: Math. Model. Numer. Anal. 31(5), 615\u2013641 (1997)","journal-title":"ESAIM: Math. Model. Numer. Anal."},{"issue":"4","key":"2522_CR11","doi-asserted-by":"crossref","first-page":"955","DOI":"10.4310\/CMS.2015.v13.n4.a6","volume":"13","author":"AL Bertozzi","year":"2015","unstructured":"Bertozzi, A.L., Kolokolnikov, T., Sun, H., Uminsky, D., Von, B.J.: Ring patterns and their bifurcations in a nonlocal model of biological swarms. Commun. Math. Sci. 13(4), 955\u2013985 (2015)","journal-title":"Commun. Math. Sci."},{"issue":"5","key":"2522_CR12","first-page":"B559","volume":"34","author":"CM Bessemoulin","year":"2012","unstructured":"Bessemoulin, C.M., Filbet, F.: A finite volume scheme for nonlinear degenerate parabolic equations. J. Sci. Comput. 34(5), B559\u2013B583 (2012)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"2522_CR13","doi-asserted-by":"crossref","first-page":"1125","DOI":"10.1093\/imanum\/dru032","volume":"35","author":"M Bessemoulin-Chatard","year":"2015","unstructured":"Bessemoulin-Chatard, M., Chainais-Hillairet, C., Filbet, F.: On discrete functional inequalities for some finite volume schemes. IMA J. Numer. Anal. 35(3), 1125\u20131149 (2015)","journal-title":"IMA J. Numer. Anal."},{"key":"2522_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-75934-0","volume-title":"The mathematical theory of finite element methods","author":"SC Brenner","year":"2008","unstructured":"Brenner, S.C., Scott, L.R.: The mathematical theory of finite element methods. Springer, New York (2008)"},{"issue":"3","key":"2522_CR15","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1016\/j.nonrwa.2006.04.002","volume":"8","author":"M Burger","year":"2007","unstructured":"Burger, M., Capasso, V., Morale, D.: On an aggregation model with long and short range interactions. Nonlinear Anal. Real World Appl. 8(3), 939\u2013958 (2007)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"2522_CR16","doi-asserted-by":"crossref","first-page":"59","DOI":"10.3934\/krm.2010.3.59","volume":"3","author":"M Burger","year":"2009","unstructured":"Burger, M., Carrillo, J.A., Wolfram, M.T.: A mixed finite element method for nonlinear diffusion equations. Kinet. Relat. Models 3, 59\u201383 (2009)","journal-title":"Kinet. Relat. Models"},{"issue":"1","key":"2522_CR17","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1007\/BF01385651","volume":"58","author":"Z Cai","year":"1990","unstructured":"Cai, Z.: On the finite volume element method. Numer. Math. 58(1), 713\u2013735 (1990)","journal-title":"Numer. Math."},{"issue":"2","key":"2522_CR18","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.matpur.2006.04.002","volume":"86","author":"V Calvez","year":"2006","unstructured":"Calvez, V., Carrillo, J.A.: Volume effects in the Keller-Segel model: energy estimates preventing blow-up. Journal de math\u00e9matiques pures et appliqu\u00e9es 86(2), 155\u2013175 (2006)","journal-title":"Journal de math\u00e9matiques pures et appliqu\u00e9es"},{"issue":"1","key":"2522_CR19","doi-asserted-by":"crossref","first-page":"233","DOI":"10.4208\/cicp.160214.010814a","volume":"17","author":"JA Carrillo","year":"2015","unstructured":"Carrillo, J.A., Chertock, A., Huang, Y.: A finite-volume method for nonlinear nonlocal equations with a gradient flow structure. Commun. Comput. Phys. 17(1), 233\u2013258 (2015)","journal-title":"Commun. Comput. Phys."},{"key":"2522_CR20","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s10208-021-09503-1","volume":"22","author":"JA Carrillo","year":"2022","unstructured":"Carrillo, J.A., Craig, K., Wang, L., Wei, C.: Primal dual methods for Wasserstein gradient flows. Found. Comut. Math. 22, 389\u2013443 (2022)","journal-title":"Found. Comut. Math."},{"key":"2522_CR21","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/s00211-020-01121-3","volume":"145","author":"JA Carrillo","year":"2020","unstructured":"Carrillo, J.A., Filbet, F., Schmidtchen, M.: Convergence of a finite volume scheme for a system of interacting species with cross-diffusion. Numer. Math. 145, 473\u2013511 (2020)","journal-title":"Numer. Math."},{"issue":"3","key":"2522_CR22","doi-asserted-by":"crossref","first-page":"613","DOI":"10.3934\/krm.2017025","volume":"10","author":"JA Carrillo","year":"2017","unstructured":"Carrillo, J.A., Huang, Y., Patacchini, F.S., Wolansky, G.: Numerical study of a particle method for gradient flows. Kinet. Relat. Models 10(3), 613\u2013641 (2017)","journal-title":"Kinet. Relat. Models"},{"issue":"2","key":"2522_CR23","first-page":"1078","volume":"78","author":"JA Carrillo","year":"2018","unstructured":"Carrillo, J.A., Huang, Y., Schmidtchen, M.: Zoology of a nonlocal cross-diffusion model for two species. J. Appl. Math. 78(2), 1078\u20131104 (2018)","journal-title":"J. Appl. Math."},{"key":"2522_CR24","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s00205-005-0386-1","volume":"179","author":"JA Carrillo","year":"2006","unstructured":"Carrillo, J.A., McCann, R.J., Villani, C.: Contractions in the 2-Wasserstein length space and thermalization of granular media. Arch. Ration. Mech. Anal. 179, 217\u2013263 (2006)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"2522_CR25","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719208","volume-title":"The finite element method for elliptic problems","author":"PG Ciarlet","year":"2002","unstructured":"Ciarlet, P.G.: The finite element method for elliptic problems. SIAM, USA (2002)"},{"issue":"300","key":"2522_CR26","doi-asserted-by":"crossref","first-page":"1681","DOI":"10.1090\/mcom3033","volume":"85","author":"K Craig","year":"2016","unstructured":"Craig, K., Bertozzi, A.: A blob method for the aggregation equation. Math. Comput. 85(300), 1681\u20131717 (2016)","journal-title":"Math. Comput."},{"key":"2522_CR27","first-page":"713","volume":"7","author":"R Eymard","year":"2000","unstructured":"Eymard, R., Gallou\u00ebt, T., Herbin, R.: Finite volume methods. Handb. Numer. Anal. 7, 713\u20131018 (2000)","journal-title":"Handb. Numer. Anal."},{"issue":"10","key":"2522_CR28","doi-asserted-by":"crossref","first-page":"2681","DOI":"10.1088\/0951-7715\/24\/10\/002","volume":"24","author":"RC Fetecau","year":"2011","unstructured":"Fetecau, R.C., Huang, Y., Kolokolnikov, T.: Swarm dynamics and equilibria for a nonlocal aggregation model. Nonlinearity 24(10), 2681 (2011)","journal-title":"Nonlinearity"},{"key":"2522_CR29","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s10013-016-0190-2","volume":"45","author":"J Garnier","year":"2017","unstructured":"Garnier, J., Papanicolaou, G., Yang, T.W.: Consensus convergence with stochastic effects. Vietnam J. Math. 45, 51\u201375 (2017)","journal-title":"Vietnam J. Math."},{"issue":"22","key":"2522_CR30","doi-asserted-by":"crossref","first-page":"226106","DOI":"10.1103\/PhysRevLett.95.226106","volume":"95","author":"D Holm","year":"2005","unstructured":"Holm, D., Putkaradze, V.: Aggregation of finite-size particles with variable mobility. Phys. Rev. Lett. 95(22), 226106 (2005)","journal-title":"Phys. Rev. Lett."},{"key":"2522_CR31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physd.2013.06.011","volume":"260","author":"T Kolokolnikov","year":"2013","unstructured":"Kolokolnikov, T., Carrillo, J.A., Bertozzi, A., Fetecau, R., Lewis, M.: Emergent behaviour in multi-particle systems with non-local interactions. Physica D: Nonlin. Phenomen 260, 1\u20134 (2013)","journal-title":"Physica D: Nonlin. Phenomen"},{"key":"2522_CR32","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1007\/s10915-016-0174-0","volume":"68","author":"H Liu","year":"2016","unstructured":"Liu, H., Wang, Z.: An entropy satisfying discontinuous Galerkin method for nonlinear fokker-planck equations. J. Sci. Comput. 68, 1217\u20131240 (2016)","journal-title":"J. Sci. Comput."},{"key":"2522_CR33","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.jcp.2016.10.008","volume":"328","author":"H Liu","year":"2017","unstructured":"Liu, H., Wang, Z.: A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems. J. Comput. Phys. 328, 413\u2013437 (2017)","journal-title":"J. Comput. Phys."},{"issue":"6","key":"2522_CR34","doi-asserted-by":"crossref","first-page":"061904","DOI":"10.1103\/PhysRevE.78.061904","volume":"78","author":"PM Lushnikov","year":"2008","unstructured":"Lushnikov, P.M., Chen, N., Alber, M.: Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact. Phys. Rev. E 78(6), 061904 (2008)","journal-title":"Phys. Rev. E"},{"issue":"1","key":"2522_CR35","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1006\/aima.1997.1634","volume":"128","author":"RJ McCann","year":"1997","unstructured":"McCann, R.J.: A convexity principle for interacting gases. Adv. Math. 128(1), 153\u2013179 (1997)","journal-title":"Adv. Math."},{"issue":"4","key":"2522_CR36","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1137\/120901866","volume":"56","author":"S Motsch","year":"2014","unstructured":"Motsch, S., Tadmor, E.: Heterophilious dynamics enhances consensus. SIAM Rev. 56(4), 577\u2013621 (2014)","journal-title":"SIAM Rev."},{"issue":"2","key":"2522_CR37","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1093\/imanum\/drl018","volume":"27","author":"N Saito","year":"2007","unstructured":"Saito, N.: Conservative upwind finite-element method for a simplified Keller-Segel system modelling chemotaxis. IMA J. Numer. Anal. 27(2), 332\u2013365 (2007)","journal-title":"IMA J. Numer. Anal."},{"key":"2522_CR38","first-page":"125","volume":"15","author":"N Saito","year":"2009","unstructured":"Saito, N.: Conservative numerical schemes for the Keller-Segel system. RIMS K\u00f4ky\u00fbroku 15, 125\u2013146 (2009)","journal-title":"RIMS K\u00f4ky\u00fbroku"},{"issue":"1","key":"2522_CR39","doi-asserted-by":"crossref","first-page":"339","DOI":"10.3934\/cpaa.2012.11.339","volume":"11","author":"N Saito","year":"2011","unstructured":"Saito, N.: Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis. Commun. Pure Appl. Anal. 11(1), 339\u2013364 (2011)","journal-title":"Commun. Pure Appl. Anal."},{"key":"2522_CR40","first-page":"18","volume":"1320","author":"N Saito","year":"2003","unstructured":"Saito, N., Suzuki, T.: A finite difference scheme to the system of self-interacting particles. RIMS K\u00f4ky\u00fbroku 1320, 18\u201328 (2003)","journal-title":"RIMS K\u00f4ky\u00fbroku"},{"issue":"1","key":"2522_CR41","first-page":"72","volume":"171","author":"N Saito","year":"2005","unstructured":"Saito, N., Suzuki, T.: Notes on finite difference schemes to a parabolic-elliptic system modelling chemotaxis. Appl. Math. Comput. 171(1), 72\u201390 (2005)","journal-title":"Appl. Math. Comput."},{"key":"2522_CR42","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.jcp.2017.09.050","volume":"352","author":"Z Sun","year":"2018","unstructured":"Sun, Z., Carrillo, J.A., Shu, C.: A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials. J. Comput. Phys. 352, 76\u2013104 (2018)","journal-title":"J. Comput. Phys."},{"key":"2522_CR43","doi-asserted-by":"crossref","first-page":"1601","DOI":"10.1007\/s11538-006-9088-6","volume":"68","author":"CM Topaz","year":"2006","unstructured":"Topaz, C.M., Bertozzi, A.L., Lewis, M.A.: A nonlocal continuum model for biological aggregation. Bull. Math. Biol. 68, 1601\u20131623 (2006)","journal-title":"Bull. Math. Biol."},{"issue":"6","key":"2522_CR44","doi-asserted-by":"crossref","first-page":"1277","DOI":"10.1051\/m2an:2000127","volume":"34","author":"G Toscani","year":"2000","unstructured":"Toscani, G.: One-dimensional kinetic models of granular flows. ESAIM: Math. Model. Numer. Anal. 34(6), 1277\u20131291 (2000)","journal-title":"ESAIM: Math. Model. Numer. Anal."},{"key":"2522_CR45","volume-title":"Matrix iterative analysis","author":"RS Varga","year":"1999","unstructured":"Varga, R.S.: Matrix iterative analysis. Springer, Berlin (1999)"},{"key":"2522_CR46","unstructured":"Villani, C.: Topics in optimal transportation. American Mathematical Soc, USA (2021)"},{"issue":"2","key":"2522_CR47","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10915-021-01466-3","volume":"87","author":"G Zhou","year":"2021","unstructured":"Zhou, G.: An analysis on the finite volume schemes and the discrete Lyapunov inequalities for the chemotaxis system. J. Sci. Comput. 87(2), 1\u201347 (2021)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"2522_CR48","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s00211-016-0793-2","volume":"135","author":"G Zhou","year":"2017","unstructured":"Zhou, G., Saito, N.: Finite volume methods for a Keller-Segel system: discrete energy, error estimates and numerical blow-up analysis. Numer. Math. 135(1), 265\u2013311 (2017)","journal-title":"Numer. Math."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-024-02522-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-024-02522-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-024-02522-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,30]],"date-time":"2024-04-30T19:09:51Z","timestamp":1714504191000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-024-02522-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,16]]},"references-count":48,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,5]]}},"alternative-id":["2522"],"URL":"https:\/\/doi.org\/10.1007\/s10915-024-02522-4","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2024,4,16]]},"assertion":[{"value":"31 October 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 February 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 April 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":"55"}}