{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:02:34Z","timestamp":1776844954391,"version":"3.51.2"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2005,1,18]],"date-time":"2005-01-18T00:00:00Z","timestamp":1106006400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2005,2]]},"DOI":"10.1007\/s00211-004-0567-0","type":"journal-article","created":{"date-parts":[[2005,1,18]],"date-time":"2005-01-18T06:50:16Z","timestamp":1106031016000},"page":"585-604","source":"Crossref","is-referenced-by-count":4,"title":["Convergence of flux vector splitting schemes with single entropy inequality for hyperbolic systems of conservation laws"],"prefix":"10.1007","volume":"99","author":[{"given":"F.","family":"Berthelin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,1,18]]},"reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"1973","DOI":"10.1137\/S0036142998343075","volume":"37","author":"Aregba-Driollet","year":"6","unstructured":"Aregba-Driollet, D., Natalini, R.: Discrete kinetic schemes for multidimensional systems of conservation laws. SIAM J. Numer. Anal. 37(6), 1973?2004 (2000)","journal-title":"SIAM J. Numer. Anal."},{"key":"CR2","doi-asserted-by":"crossref","first-page":"605","DOI":"10.5802\/afst.974","volume":"9","author":"Berthelin","year":"2000","unstructured":"Berthelin, F., Bouchut, F.: Solution with finite energy to a BGK system relaxing to isentropic gas dynamics. Annales de la Facult\u00e9 des Sciences de Toulouse 9, 605?630 (2000)","journal-title":"Annales de la Facult\u00e9 des Sciences de Toulouse"},{"key":"CR3","doi-asserted-by":"crossref","first-page":"153","DOI":"10.3233\/ASY-2002-520","volume":"31","author":"Berthelin","year":"2","unstructured":"Berthelin, F., Bouchut, F.: Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics. Asymptotic Analysis, 31(2), 153?176 (2002)","journal-title":"Asymptotic Analysis,"},{"key":"CR4","doi-asserted-by":"crossref","first-page":"313","DOI":"10.4310\/MAA.2002.v9.n2.a7","volume":"9","author":"Berthelin","year":"2","unstructured":"Berthelin, F., Bouchut, F.: Relaxation to isentropic gas dynamics for a BGK system with single kinetic entropy. Meth. and Appl. of Analysis 9(2), 313?327 (2002)","journal-title":"Meth. and Appl. of Analysis"},{"key":"CR5","doi-asserted-by":"crossref","unstructured":"Bouchut, F.: Construction of BGK models with a family of kinetic entropies for a given system of conservation laws. J. Statist. Phys. 95(1?2), 113?170 (1999)","DOI":"10.1023\/A:1004525427365"},{"key":"CR6","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1007\/s00211-002-0426-9","volume":"94","author":"Bouchut","year":"2003","unstructured":"Bouchut, F.: Entropy satisfying flux vector splittings and kinetic BGK models. Numer. Math. 94, 623?672 (2003)","journal-title":"Numer. Math."},{"key":"CR7","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/0022-0396(83)90067-0","volume":"50","author":"Brenier","year":"3","unstructured":"Brenier, Y.: R\u00e9solution d?\u00e9quations d?\u00e9volution quasilin\u00e9aires en dimension N d?espace \u00e0 l?aide d?\u00e9quations lin\u00e9aires en dimension N+1. J. Differential Equations 50(3), 375?390 (1983)","journal-title":"J. Differential Equations"},{"key":"CR8","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1137\/0721063","volume":"21","author":"Brenier","year":"6","unstructured":"Brenier, Y.: Averaged multivalued solutions for scalar conservation laws. SIAM J. Numer. Anal. 21(6), 1013?1037 (1984)","journal-title":"SIAM J. Numer. Anal."},{"key":"CR9","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/BF01385691","volume":"66","author":"Champier","year":"2","unstructured":"Champier, S., Gallou\u00ebt, T., Herbin, R.: Convergence of an upstream finite volume scheme for a nonlinear hyperbolic equation on a triangular mesh. Numer. Math. 66(2), 139?157 (1993)","journal-title":"Numer. Math."},{"key":"CR10","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1002\/cpa.3160480703","volume":"48","author":"Chen","year":"7","unstructured":"Chen, G.-Q., LeFloch, P.G.: Entropy flux-splittings for hyperbolic conservation laws I, General framework. Commun. Pure Appl. Math. 48(7), 691?729 (1995)","journal-title":"Commun. Pure Appl. Math."},{"key":"CR11","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1142\/S0218202596000444","volume":"6","author":"Desvillettes","year":"8","unstructured":"Desvillettes, L., Mischler, S.: About the splitting algorithm for Boltzmann and B.G.K. equations. Math. Models Methods Appl. Sci. 6(8), 1079?1101 (1996)","journal-title":"G.K. equations. Math. Models Methods Appl. Sci."},{"key":"CR12","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/BF00251724","volume":"82","author":"DiPerna","year":"1983","unstructured":"DiPerna, R.J.: Convergence of approximate solutions to conservation laws. Arch. Rational Mech. Anal. 82, 27?70 (1983)","journal-title":"Arch. Rational Mech. Anal."},{"key":"CR13","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1093\/imanum\/18.4.563","volume":"18","author":"Eymard","year":"4","unstructured":"Eymard, R., Gallou\u00ebt, T., Ghilani, M., Herbin, R.: Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes. IMA J. Numer. Anal. 18(4), 563?594 (1998)","journal-title":"IMA J. Numer. Anal."},{"key":"CR14","doi-asserted-by":"crossref","unstructured":"Eymard, R., Gallou\u00ebt, T., Herbin, R.: Finite volume methods, Handbook of numerical analysis, Vol. VII. Handb. Numer. Anal. VII, North-Holland, Amsterdam, 2000 pp. 713?1020","DOI":"10.1016\/S1570-8659(00)07005-8"},{"key":"CR15","doi-asserted-by":"crossref","unstructured":"Godlewski, E., Raviart, P.-A.: Numerical approximation of hyperbolic systems of conservation laws. Applied Mathematical Sciences, 118, Springer-Verlag, New York, 1996","DOI":"10.1007\/978-1-4612-0713-9"},{"key":"CR16","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1090\/S0025-5718-00-01256-4","volume":"70","author":"Gosse","year":"234","unstructured":"Gosse, L., Tzavaras, A.E.: Convergence of relaxation schemes to the equations of elastodynamics. Math. Comp. 70(234), 555?577 (2001)","journal-title":"Math. Comp."},{"key":"CR17","doi-asserted-by":"crossref","unstructured":"Hwang, S., Tzavaras, A.E.: Kinetic decomposition of approximate solutions to conservation laws: applications to relaxation and diffusion-dispersion approximations. Comm. Partial Differential Equations 27(5?6), 1229?1254 (2002)","DOI":"10.1081\/PDE-120004900"},{"key":"CR18","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/PL00005436","volume":"88","author":"Lattanzio","year":"1","unstructured":"Lattanzio, C., Serre, D.: Convergence of a relaxation scheme for hyperbolic systems of conservation laws. Numer. Math. 88(1), 121?134 (2001)","journal-title":"Numer. Math."},{"key":"CR19","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/S0294-1449(99)00105-5","volume":"17","author":"Serre","year":"2000","unstructured":"Serre, D.: Relaxation semi-lin\u00e9aire et cin\u00e9tique des syst\u00e8mes de lois de conservation. Ann. Inst. H. Poincar\u00e9 Anal. non lin\u00e9aire 17, 169?192 (2000)","journal-title":"Ann. Inst. H. Poincar\u00e9 Anal. non lin\u00e9aire"},{"key":"CR20","unstructured":"Tartar, L.: Compensated compactness and applications to partial differential equations. Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV, Res. Notes in Math. 39, Pitman, Boston, Mass.-London, 1979, pp. 136?212"},{"key":"CR21","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/s002050050139","volume":"146","author":"Tzavaras","year":"2","unstructured":"Tzavaras, A.E.: Materials with internal variables and relaxation to conservation laws. Arch. Ration. Mech. Anal. 146(2), 129?155 (1999)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"CR22","first-page":"347","volume":"48","author":"Vasseur","year":"1","unstructured":"Vasseur, A.: Convergence of a semi-discrete kinetic scheme for the system of isentropic gas dynamics with ?=3. Indiana Univ. Math. J. 48(1), 347?364 (1999)","journal-title":"Indiana Univ. Math. J."},{"key":"CR23","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1137\/S0036142996313610","volume":"36","author":"Vasseur","year":"2","unstructured":"Vasseur, A.: Kinetic semidiscretization of scalar conservation laws and convergence by using averaging lemmas. SIAM J. Numer. Anal. 36(2), 465?474 (1999)","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-004-0567-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-004-0567-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-004-0567-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,22]],"date-time":"2024-12-22T16:58:18Z","timestamp":1734886698000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-004-0567-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,1,18]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2005,2]]}},"alternative-id":["567"],"URL":"https:\/\/doi.org\/10.1007\/s00211-004-0567-0","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,1,18]]}}}