{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T17:53:47Z","timestamp":1773424427771,"version":"3.50.1"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T00:00:00Z","timestamp":1551916800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["P27352"],"award-info":[{"award-number":["P27352"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["P30000"],"award-info":[{"award-number":["P30000"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["F65"],"award-info":[{"award-number":["F65"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["W1245"],"award-info":[{"award-number":["W1245"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s10444-019-09674-0","type":"journal-article","created":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T04:48:41Z","timestamp":1551934121000},"page":"1469-1498","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Convergence of an implicit Euler Galerkin scheme for Poisson\u2013Maxwell\u2013Stefan systems"],"prefix":"10.1007","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0633-8929","authenticated-orcid":false,"given":"Ansgar","family":"J\u00fcngel","sequence":"first","affiliation":[]},{"given":"Oliver","family":"Leingang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,3,7]]},"reference":[{"key":"9674_CR1","doi-asserted-by":"crossref","unstructured":"Bothe, D., et al.: On the Maxwell-Stefan Equations to Multicomponent Diffusion. In: Escher, J. (ed.) Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, pp. 81\u201393. Springer, Basel (2011)","DOI":"10.1007\/978-3-0348-0075-4_5"},{"key":"9674_CR2","doi-asserted-by":"publisher","first-page":"1757","DOI":"10.1007\/s00707-014-1275-1","volume":"226","author":"D Bothe","year":"2015","unstructured":"Bothe, D., Dreyer, W.: Continuum thermodynamics of chemically reacting fluid mixtures. Acta Mech. 226, 1757\u20131805 (2015)","journal-title":"Acta Mech."},{"key":"9674_CR3","doi-asserted-by":"publisher","first-page":"1427","DOI":"10.3934\/dcdsb.2012.17.1427","volume":"17","author":"L Boudin","year":"2012","unstructured":"Boudin, L., Grec, B., Salvarani, F.: A mathematical and numerical analysis of the Maxwell\u2013Stefan diffusion equations. Discret. Cont. Dyn. Sys. B 17, 1427\u20131440 (2012)","journal-title":"Discret. Cont. Dyn. Sys. B"},{"key":"9674_CR4","doi-asserted-by":"publisher","first-page":"137","DOI":"10.3934\/krm.2013.6.137","volume":"6","author":"L Boudin","year":"2013","unstructured":"Boudin, L., Grec, B., Pavi\u0107, M., Salvarani, F.: Diffusion asymptotics of a kinetic model for gaseous mixtures. Kinetic Related Model 6, 137\u2013157 (2013)","journal-title":"Kinetic Related Model"},{"key":"9674_CR5","unstructured":"Canc\u00e8s, C., Nabet, F., Vohralik, M.: Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations. Preprint, 2018. hal-01894884"},{"key":"9674_CR6","doi-asserted-by":"publisher","first-page":"665","DOI":"10.1002\/nme.2103","volume":"73","author":"B Carnes","year":"2008","unstructured":"Carnes, B., Carey, G.: Local boundary value problems for the error in FE approximation of non-linear diffusion systems. Intern. J. Numer. Meth Engrg. 73, 665\u2013684 (2008)","journal-title":"Intern. J. Numer. Meth Engrg."},{"key":"9674_CR7","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1515\/cmam-2015-0018","volume":"15","author":"P Chatzipantelidis","year":"2015","unstructured":"Chatzipantelidis, P., Horv\u00e1th, Z., Thom\u00e9e, V.: On preservation of positivity in some finite element methods for the heat equation. Comput. Meth. Appl. Math. 15, 417\u2013437 (2015)","journal-title":"Comput. Meth. Appl. Math."},{"key":"9674_CR8","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1007\/s00220-015-2472-z","volume":"340","author":"X Chen","year":"2015","unstructured":"Chen, X., J\u00fcngel, A.: Analysis of an incompressible Navier\u2013Stokes\u2013Maxwell\u2013Stefan system. Commun. Math Phys. 340, 471\u2013497 (2015)","journal-title":"Commun. Math Phys."},{"key":"9674_CR9","unstructured":"Daus, E., J\u00fcngel, A., Tang, B.-Q.: Exponential time decay of solutions to reaction-cross-diffusion systems of Maxwell\u2013Stefan type. Submitted for publication, arXiv: 1802.10274 (2018)"},{"key":"9674_CR10","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1515\/ans-2007-0309","volume":"7","author":"L Desvillettes","year":"2007","unstructured":"Desvillettes, L., Fellner, K., Pierre, M., Vovelle, J.: Global existence for quadratic systems of reaction-diffusion. Adv Nonlin. Stud. 7, 491\u2013511 (2007)","journal-title":"Adv Nonlin. Stud."},{"key":"9674_CR11","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1016\/j.compfluid.2014.12.017","volume":"109","author":"K Dieter-Kisling","year":"2015","unstructured":"Dieter-Kisling, K., Marschall, H., Bothe, D.: Numerical method for coupled interfacial surfactant transport on dynamic surface meshes of general topology. Comput. Fluids 109, 168\u2013184 (2015)","journal-title":"Comput. Fluids"},{"key":"9674_CR12","doi-asserted-by":"publisher","first-page":"3072","DOI":"10.1016\/j.na.2011.12.004","volume":"75","author":"M Dreher","year":"2012","unstructured":"Dreher, M., J\u00fcngel, A.: Compact families of piecewise constant functions in L p(0,T; B). Nonlin. Anal. 75, 3072\u20133077 (2012)","journal-title":"Nonlin. Anal."},{"key":"9674_CR13","unstructured":"Dreyer, W., Druet, P.-E., Gajewski, P., Guhlke, C.: Analysis of improved Nernst-Planck-Poisson models of compressible isothermal electrolytes. Part I Derivation of the model and survey of the results. WIAS Berlin, Germany, preprint no. 2395 (2017)"},{"key":"9674_CR14","doi-asserted-by":"publisher","first-page":"7075","DOI":"10.1039\/c3cp44390f","volume":"15","author":"W Dreyer","year":"2013","unstructured":"Dreyer, W., Guhlke, C., M\u00fcller, R.: Overcoming the shortcomings of the Nernst-Planck-Poisson model. Phys. Chem. Chem Phys. 15, 7075\u20137086 (2013)","journal-title":"Phys. Chem. Chem Phys."},{"key":"9674_CR15","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1002\/aic.690080112","volume":"8","author":"J Duncan","year":"1962","unstructured":"Duncan, J., Toor, H.: An experimental study of three component gas diffusion. AIChE J. 8, 38\u201341 (1962)","journal-title":"AIChE J."},{"key":"9674_CR16","doi-asserted-by":"publisher","first-page":"1120","DOI":"10.1137\/070706276","volume":"31","author":"S Gadau","year":"2008","unstructured":"Gadau, S., J\u00fcngel, A.: A three-dimensional mixed finite-element approximation of the semiconductor energy-transport equations. SIAM J. Sci Comput. 31, 1120\u20131140 (2008)","journal-title":"SIAM J. Sci Comput."},{"key":"9674_CR17","doi-asserted-by":"publisher","first-page":"590","DOI":"10.1007\/BF01051339","volume":"27","author":"V Galkin","year":"1993","unstructured":"Galkin, V., Makashev, N.: Modification of the first approximation of the Chapman-Enskog method for a gas mixture. Fluid Dynam. 27, 590\u2013596 (1993). Translated from em Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza 4 (1992), 178-185 (Russian)","journal-title":"Fluid Dynam."},{"key":"9674_CR18","doi-asserted-by":"publisher","first-page":"1092913, 16.","DOI":"10.1080\/23311835.2015.1092913","volume":"2","author":"J Geiser","year":"2015","unstructured":"Geiser, J.: Iterative solvers for the Maxwell-Stefan diffusion equations: methods and applications in plasma and particle transport. Cogent Math. 2, 1092913, 16. (2015)","journal-title":"Cogent Math."},{"key":"9674_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1580-6","volume-title":"Multicomponent Flow Modeling","author":"V Giovangigli","year":"1999","unstructured":"Giovangigli, V.: Multicomponent Flow Modeling. Basel, Birkh\u00e4user (1999)"},{"key":"9674_CR20","doi-asserted-by":"publisher","first-page":"1415","DOI":"10.1002\/(SICI)1099-1476(199810)21:15<1415::AID-MMA2>3.0.CO;2-D","volume":"21","author":"V Giovangigli","year":"1998","unstructured":"Giovangigli, V., Massot, M.: The local Cauchy problem for multicomponent flows in full vibrational non-equilibrium. Math. Meth. Appl. Sci. 21, 1415\u20131439 (1998)","journal-title":"Math. Meth. Appl. Sci."},{"key":"9674_CR21","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1016\/j.na.2016.07.010","volume":"159","author":"M Herberg","year":"2017","unstructured":"Herberg, M., Meyries, M., Pr\u00fcss, J., Wilke, M.: Reaction-diffusion systems of Maxwell\u2013Stefan type with reversible mass-action kinetics. Nonlin. Anal. 159, 264\u2013284 (2017)","journal-title":"Nonlin. Anal."},{"key":"9674_CR22","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/j.na.2017.03.019","volume":"159","author":"H Hutridurga","year":"2017","unstructured":"Hutridurga, H., Salvarani, F.: Maxwell\u2013Stefan diffusion asymptotics for gas mixtures in non-isothermal setting. Nonlin. Anal. 159, 285\u2013297 (2017)","journal-title":"Nonlin. Anal."},{"key":"9674_CR23","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.aml.2017.06.007","volume":"75","author":"H Hutridurga","year":"2018","unstructured":"Hutridurga, H., Salvarani, F.: Existence and uniqueness analysis of a non-isothermal cross-diffusion system of Maxwell-Stefan type. Appl. Math. Lett. 75, 108\u2013113 (2018)","journal-title":"Appl. Math. Lett."},{"key":"9674_CR24","doi-asserted-by":"publisher","first-page":"1963","DOI":"10.1088\/0951-7715\/28\/6\/1963","volume":"28","author":"A J\u00fcngel","year":"2015","unstructured":"J\u00fcngel, A.: The boundedness-by-entropy method for cross-diffusion systems. Nonlinearity 28, 1963\u20132001 (2015)","journal-title":"Nonlinearity"},{"key":"9674_CR25","doi-asserted-by":"publisher","first-page":"1250009, 26","DOI":"10.1142\/S0218202512500091","volume":"22","author":"A J\u00fcngel","year":"2012","unstructured":"J\u00fcngel, A., Stelzer, I.: Entropy structure of a cross-diffusion tumor-growth model. Math. Models Meth. Appl. Sci. 22, 1250009, 26 (2012)","journal-title":"Math. Models Meth. Appl. Sci."},{"key":"9674_CR26","doi-asserted-by":"publisher","first-page":"2421","DOI":"10.1137\/120898164","volume":"45","author":"A J\u00fcngel","year":"2013","unstructured":"J\u00fcngel, A., Stelzer, I.: Existence analysis of Maxwell-Stefan systems for multicomponent mixtures. SIAM J. Math Anal. 45, 2421\u20132440 (2013)","journal-title":"SIAM J. Math Anal."},{"key":"9674_CR27","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1021\/jp900760c","volume":"114","author":"E Leonardia","year":"2010","unstructured":"Leonardia, E., Angeli, C.: On the Maxwell\u2013Stefan approach to diffusion: a general resolution in the transient regime for one-dimensional systems. J. Phys. Chem. B 114, 151\u2013164 (2010)","journal-title":"J. Phys. Chem. B"},{"key":"9674_CR28","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1135\/cccc19920687","volume":"57","author":"J-P Loos","year":"1992","unstructured":"Loos, J.-P., Verheijen, P., Moulin, J.: Numerical simulation of the generalized Maxwell\u2013Stefan model for multicomponent diffusion in microporous sorbents. Collect. Czech. Chem Commun. 57, 687\u2013697 (1992)","journal-title":"Collect. Czech. Chem Commun."},{"key":"9674_CR29","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.matpur.2015.02.003","volume":"104","author":"M Marion","year":"2015","unstructured":"Marion, M., Temam, R.: Global existence for fully nonlinear reaction-diffusion systems describing multicomponent reactive flows. J. Math Pures Appl. 104, 102\u2013138 (2015)","journal-title":"J. Math Pures Appl."},{"key":"9674_CR30","first-page":"49","volume":"157","author":"C Maxwell","year":"1866","unstructured":"Maxwell, C.: On the dynamical theory of gases. Phil. Trans. Roy. Soc. Lond. 157, 49\u201388 (1866)","journal-title":"Phil. Trans. Roy. Soc. Lond."},{"key":"9674_CR31","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1016\/j.cma.2014.07.010","volume":"279","author":"M McLeod","year":"2014","unstructured":"McLeod, M., Bourgault, Y.: Mixed finite element methods for addressing multi-species diffusion using the Maxwell-Stefan equations. Comput. Meth. Appl. Mech Engrg. 279, 515\u2013535 (2014)","journal-title":"Comput. Meth. Appl. Mech Engrg."},{"key":"9674_CR32","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1515\/zpch-1889-0412","volume":"4","author":"W Nernst","year":"1889","unstructured":"Nernst, W.: Die elektromotorische Wirksamkeit der Ionen. Z. Phys. Chem. 4, 129\u2013181 (1889)","journal-title":"Z. Phys. Chem."},{"key":"9674_CR33","doi-asserted-by":"publisher","first-page":"3525","DOI":"10.1016\/j.jcp.2011.02.001","volume":"230","author":"K Peerenboom","year":"2011","unstructured":"Peerenboom, K., van Dijk, J., Boonkkamp, J., Liu, L., Goedheer, W., van der Mullen, J.: Mass conservative finite volume discretization of the continuity equations in multi-component mixtures. J. Comput. Phys. 230, 3525\u20133537 (2011)","journal-title":"J. Comput. Phys."},{"key":"9674_CR34","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1002\/andp.18902760802","volume":"276","author":"M Planck","year":"1890","unstructured":"Planck, M.: \u00dcber die Potentialdifferenz zwischen zwei verd\u00fcnnten L\u00f6sungen bin\u00e4rer Electrolyte. Ann. Phys. 276, 561\u2013576 (1890)","journal-title":"Ann. Phys."},{"key":"9674_CR35","doi-asserted-by":"publisher","first-page":"A33","DOI":"10.1149\/1.3509776","volume":"158","author":"S Psaltis","year":"2011","unstructured":"Psaltis, S., Farrell, T.: Comparing charge transport predictions for a ternary electrolyte using the Maxwell\u2013Stefan and Nernst\u2013Planck equations. J. Electrochem. Soc. 158, A33\u2013A42 (2011)","journal-title":"J. Electrochem. Soc."},{"key":"9674_CR36","unstructured":"Salvarani, F., Soares, J.: On the relaxation of the Maxwell\u2013Stefan system to linear diffusion. Appl. Math. Lett. 85, 15\u201321 (2018)"},{"key":"9674_CR37","first-page":"63","volume":"63","author":"J Stefan","year":"1871","unstructured":"Stefan, J.: \u00dcber das Gleichgewicht und Bewegung, insbesondere die Diffusion von Gasgemengen. Sitzungsberichte Kaiserl. Akad. Wiss. Wien 63, 63\u2013124 (1871)","journal-title":"Sitzungsberichte Kaiserl. Akad. Wiss. Wien"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-019-09674-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-019-09674-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-019-09674-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T03:19:10Z","timestamp":1663039150000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-019-09674-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,7]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["9674"],"URL":"https:\/\/doi.org\/10.1007\/s10444-019-09674-0","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,7]]},"assertion":[{"value":"30 August 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 February 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 March 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}