{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:18:31Z","timestamp":1773249511784,"version":"3.50.1"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2011,12,22]],"date-time":"2011-12-22T00:00:00Z","timestamp":1324512000000},"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":[[2012,7]]},"DOI":"10.1007\/s00211-011-0443-7","type":"journal-article","created":{"date-parts":[[2011,12,21]],"date-time":"2011-12-21T05:34:25Z","timestamp":1324445665000},"page":"545-563","source":"Crossref","is-referenced-by-count":48,"title":["A minimum entropy principle of high order schemes for gas dynamics equations"],"prefix":"10.1007","volume":"121","author":[{"given":"Xiangxiong","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Chi-Wang","family":"Shu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,12,22]]},"reference":[{"key":"443_CR1","doi-asserted-by":"crossref","first-page":"1241","DOI":"10.1137\/0916072","volume":"16","author":"M.H. Carpenter","year":"1995","unstructured":"Carpenter M.H., Gottlieb D., Abarbanel S., Don W.-S.: The theoretical accuracy of Runge\u2013Kutta time discretizations for the initial boundary value problem: a study of the boundary error. SIAM J. Scientific Comput. 16, 1241\u20131252 (1995)","journal-title":"SIAM J. Scientific Comput."},{"key":"443_CR2","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/0021-9991(89)90183-6","volume":"84","author":"B. Cockburn","year":"1989","unstructured":"Cockburn B., Lin S.-Y., Shu C.-W.: TVB Runge\u2013Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one dimensional systems. J. Comput. Phys. 84, 90\u2013113 (1989)","journal-title":"J. Comput. Phys."},{"key":"443_CR3","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s10915-008-9239-z","volume":"38","author":"S. Gottlieb","year":"2009","unstructured":"Gottlieb S., Ketcheson D.I., Shu C.-W.: High order strong stability preserving time discretizations. J. Scientific Comput. 38, 251\u2013289 (2009)","journal-title":"J. Scientific Comput."},{"key":"443_CR4","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1137\/S003614450036757X","volume":"43","author":"S. Gottlieb","year":"2001","unstructured":"Gottlieb S., Shu C.-W., Tadmor E.: Strong stability preserving high order time discretization methods. SIAM Rev. 43, 89\u2013112 (2001)","journal-title":"SIAM Rev."},{"key":"443_CR5","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/0021-9991(83)90118-3","volume":"49","author":"A. Harten","year":"1983","unstructured":"Harten A.: On the symmetric form of systems of conservation laws with entropy. J. Comput. Phys. 49, 151\u2013164 (1983)","journal-title":"J. Comput. Phys."},{"key":"443_CR6","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1090\/S0025-5718-1994-1208223-4","volume":"62","author":"B. Khobalatte","year":"1994","unstructured":"Khobalatte B., Perthame B.: Maximum principle on the entropy and second-order kinetic schemes. Math. Comput. 62, 119\u2013131 (1994)","journal-title":"Math. Comput."},{"key":"443_CR7","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/s002110050187","volume":"73","author":"B. Perthame","year":"1996","unstructured":"Perthame B., Shu C.-W.: On positivity preserving finite volume schemes for Euler equations. Numerische Mathematik 73, 119\u2013130 (1996)","journal-title":"Numerische Mathematik"},{"key":"443_CR8","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1137\/0909073","volume":"9","author":"C.-W. Shu","year":"1988","unstructured":"Shu C.-W.: Total-variation-diminishing time discretizations. SIAM J. Scientific Stat. Comput. 9, 1073\u20131084 (1988)","journal-title":"SIAM J. Scientific Stat. Comput."},{"key":"443_CR9","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/0021-9991(88)90177-5","volume":"77","author":"C.-W. Shu","year":"1988","unstructured":"Shu C.-W., Osher S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77, 439\u2013471 (1988)","journal-title":"J. Comput. Phys."},{"key":"443_CR10","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/0021-9991(89)90222-2","volume":"83","author":"C.-W. Shu","year":"1989","unstructured":"Shu C.-W., Osher S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes, II. J. Comput. Phys. 83, 32\u201378 (1989)","journal-title":"J. Comput. Phys."},{"key":"443_CR11","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0168-9274(86)90029-2","volume":"2","author":"E. Tadmor","year":"1986","unstructured":"Tadmor E.: A minimum entropy principle in the gas dynamics equations. Appl. Numer. Math. 2, 211\u2013219 (1986)","journal-title":"Appl. Numer. Math."},{"key":"443_CR12","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1016\/j.jcp.2011.10.002","volume":"231","author":"C. Wang","year":"2012","unstructured":"Wang C., Zhang X., Shu C.-W., Ning J.: Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations. J. Comput. Phys. 231, 653\u2013665 (2012)","journal-title":"J. Comput. Phys."},{"key":"443_CR13","doi-asserted-by":"crossref","first-page":"3091","DOI":"10.1016\/j.jcp.2009.12.030","volume":"229","author":"X. Zhang","year":"2010","unstructured":"Zhang X., Shu C.-W.: On maximum-principle-satisfying high order schemes for scalar conservation laws. J. Comput. Phys. 229, 3091\u20133120 (2010)","journal-title":"J. Comput. Phys."},{"key":"443_CR14","doi-asserted-by":"crossref","first-page":"8918","DOI":"10.1016\/j.jcp.2010.08.016","volume":"229","author":"X. Zhang","year":"2010","unstructured":"Zhang X., Shu C.-W.: On positivity preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes. J. Comput. Phys. 229, 8918\u20138934 (2010)","journal-title":"J. Comput. Phys."},{"key":"443_CR15","unstructured":"Zhang, X., Xia, Y., Shu, C.-W.: Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes. J. Scientific Comput. (in press)"},{"key":"443_CR16","doi-asserted-by":"crossref","first-page":"2752","DOI":"10.1098\/rspa.2011.0153","volume":"467","author":"X. Zhang","year":"2011","unstructured":"Zhang X., Shu C.-W.: Maximum-principle-satisfying and positivity-preserving high order schemes for conservation laws: survey and new developments. Proc Royal Soc. A 467, 2752\u20132776 (2011)","journal-title":"Proc Royal Soc. A"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-011-0443-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-011-0443-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-011-0443-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T16:22:46Z","timestamp":1558628566000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-011-0443-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12,22]]},"references-count":16,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,7]]}},"alternative-id":["443"],"URL":"https:\/\/doi.org\/10.1007\/s00211-011-0443-7","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,12,22]]}}}