{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T08:16:39Z","timestamp":1758269799828},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2016,5,7]],"date-time":"2016-05-07T00:00:00Z","timestamp":1462579200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2017,2]]},"DOI":"10.1007\/s00211-016-0807-0","type":"journal-article","created":{"date-parts":[[2016,5,7]],"date-time":"2016-05-07T15:09:24Z","timestamp":1462633764000},"page":"493-519","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A robust high-order Lagrange-projection like scheme with large time steps for the isentropic Euler equations"],"prefix":"10.1007","volume":"135","author":[{"given":"Florent","family":"Renac","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,5,7]]},"reference":[{"key":"807_CR1","doi-asserted-by":"crossref","first-page":"2221","DOI":"10.1090\/S0025-5718-2015-02957-3","volume":"84","author":"F Berthelin","year":"2015","unstructured":"Berthelin, F., Goudon, T., Minjeaud, S.: Kinetic schemes on staggered grids for barotropic Euler models: entropy-stability analysis. Math. Comput. 84, 2221\u20132262 (2015)","journal-title":"Math. Comput."},{"key":"807_CR2","first-page":"1","volume":"11","author":"C Berthon","year":"2014","unstructured":"Berthon, C., Desveaux, V.: An entropy preserving MOOD scheme for the Euler equations. Int. J. Finite Vol. 11, 1\u201339 (2014)","journal-title":"Int. J. Finite Vol."},{"key":"807_CR3","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/j.jcp.2006.02.028","volume":"218","author":"C Berthon","year":"2006","unstructured":"Berthon, C.: Robustness of MUSCL schemes for 2D unstructured meshes. J. Comput. Phys. 218, 495\u2013509 (2006)","journal-title":"J. Comput. Phys."},{"key":"807_CR4","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1090\/S0025-5718-96-00752-1","volume":"65","author":"F Bouchut","year":"1996","unstructured":"Bouchut, F., Bourdarias, Ch., Perthame, B.: A MUSCL method satisfying all the numerical entropy inequalities. Math. Comput. 65, 1439\u20131461 (1996)","journal-title":"Math. Comput."},{"key":"807_CR5","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/s00211-005-0612-7","volume":"101","author":"C Chalons","year":"2005","unstructured":"Chalons, C., Coquel, F.: Navier\u2013Stokes equations with several independent pressure laws and explicit predictor-corrector schemes. Numer. Math. 101, 451\u2013478 (2005)","journal-title":"Numer. Math."},{"key":"807_CR6","doi-asserted-by":"crossref","first-page":"872","DOI":"10.1016\/j.jmaa.2008.07.034","volume":"348","author":"C Chalons","year":"2008","unstructured":"Chalons, C., Coulombel, J.F.: Relaxation approximation of the Euler equations. J. Math. Anal. Appl. 348, 872\u2013893 (2008)","journal-title":"J. Math. Anal. Appl."},{"key":"807_CR7","doi-asserted-by":"crossref","first-page":"A2874","DOI":"10.1137\/130908671","volume":"35","author":"C Chalons","year":"2013","unstructured":"Chalons, C., Girardin, M., Kokh, S.: Large time step and asymptotic preserving numerical schemes for the gas dynamics equations with source terms. SIAM J. Sci. Comput. 35, A2874\u2013A2902 (2013)","journal-title":"SIAM J. Sci. Comput."},{"key":"807_CR8","first-page":"411","volume":"52","author":"B Cockburn","year":"1989","unstructured":"Cockburn, B., Shu, C.W.: TVB Runge\u2013Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: general framework. Math. Comput. 52, 411\u2013435 (1989)","journal-title":"Math. Comput."},{"key":"807_CR9","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1023\/A:1012873910884","volume":"16","author":"B Cockburn","year":"2001","unstructured":"Cockburn, B., Shu, C.W.: Runge\u2013Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16, 173\u2013261 (2001)","journal-title":"J. Sci. Comput."},{"key":"807_CR10","doi-asserted-by":"crossref","unstructured":"Coquel, F., Godlewski, E., In, A., Perthame, B., Rascle, P.: Some new Godunov and relaxation methods for two-phase flow problems. In: Godunov Methods. Kluwer\/Plenum, New York (2001)","DOI":"10.1007\/978-1-4615-0663-8_18"},{"key":"807_CR11","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1002\/fld.1104","volume":"50","author":"F Coquel","year":"2006","unstructured":"Coquel, F., Helluy, P., Schneider, J.: Second-order entropy diminishing scheme for the Euler equations. Int. J. Numer. Methods Fluids 50, 1029\u20131061 (2006)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"807_CR12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s002110050205","volume":"74","author":"F Coquel","year":"1996","unstructured":"Coquel, F., LeFloch, P.G.: An entropy satisfying MUSCL scheme for systems of conservation laws. Numer. Math. 74, 1\u201333 (1996)","journal-title":"Numer. Math."},{"key":"807_CR13","doi-asserted-by":"crossref","first-page":"1493","DOI":"10.1090\/S0025-5718-10-02339-2","volume":"79","author":"F Coquel","year":"2010","unstructured":"Coquel, F., Long-Nguyen, Q., Postel, M., Tran, Q.H.: Entropy-satisfying relaxation method with large time-steps for Euler IBVPs. Math. Comput. 79, 1493\u20131533 (2010)","journal-title":"Math. Comput."},{"key":"807_CR14","doi-asserted-by":"crossref","unstructured":"Godlewski, E., Raviart, P.-A.: Numerical approximation of hyperbolic systems of conservation laws. In: Applied Mathematical Sciences, vol. 118. Springer, New-York (1996)","DOI":"10.1007\/978-1-4612-0713-9"},{"key":"807_CR15","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1002\/cpa.3160480303","volume":"48","author":"S Jin","year":"1995","unstructured":"Jin, S., Xin, Z.P.: The relaxation schemes for systems of conservation laws in arbitrary space dimension. Commun. Pure Appl. Math. 48, 235\u2013276 (1995)","journal-title":"Commun. Pure Appl. Math."},{"key":"807_CR16","doi-asserted-by":"crossref","unstructured":"Kroll, N., Bieler, H., Deconinck, H., Couaillier, V., van der Ven H., Sorensen, K. (eds.): ADIGMA\u2014a European initiative on the development of adaptive higher-order variational methods for aerospace applications. In: Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 113. Springer, New York (2010)","DOI":"10.1007\/978-3-642-03707-8"},{"key":"807_CR17","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1007\/s10915-010-9372-3","volume":"44","author":"DA Kopriva","year":"2010","unstructured":"Kopriva, D.A., Gassner, G.: On the quadrature and weak form choices in collocation type discontinuous Galerkin spectral element methods. J. Sci. Comput. 44, 136\u2013155 (2010)","journal-title":"J. Sci. Comput."},{"key":"807_CR18","doi-asserted-by":"crossref","unstructured":"Lesaint, P., Raviart, P.-A.: On a finite element method for solving the neutron transport equation. In: de Boor (ed.) Mathematical Aspects of Finite Elements in Partial Differential Equations, pp. 89\u2013123. Academic Press, New York (1974)","DOI":"10.1016\/B978-0-12-208350-1.50008-X"},{"key":"807_CR19","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. Numer. Math. 73, 119\u2013130 (1996)","journal-title":"Numer. Math."},{"key":"807_CR20","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1016\/j.jcp.2005.07.011","volume":"26","author":"J Qiu","year":"2006","unstructured":"Qiu, J., Khoo, B.C., Shu, C.-W.: A numerical study for the performance of the Runge\u2013Kutta discontinous Galerkin method based on different numerical fluxes. J. Comput. Phys. 26, 540\u2013565 (2006)","journal-title":"J. Comput. Phys."},{"key":"807_CR21","unstructured":"Reed, W.H., Hill, T.R.: Triangular mesh methods for the neutron transport equation. Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory, NM (1973)"},{"key":"807_CR22","doi-asserted-by":"crossref","first-page":"1690","DOI":"10.1137\/14097906X","volume":"53","author":"F Renac","year":"2015","unstructured":"Renac, F.: Stationary discrete shock profiles for scalar conservation laws with a discontinuous Galerkin method. SIAM J. Numer. Anal. 53, 1690\u20131715 (2015)","journal-title":"SIAM J. Numer. Anal."},{"key":"807_CR23","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.jcp.2013.05.043","volume":"251","author":"F Renac","year":"2013","unstructured":"Renac, F., G\u00e9rald, S., Marmignon, C., Coquel, F.: Fast time implicit-explicit discontinuous Galerkin method for the compressible Navier\u2013Stokes equations. J. Comput. Phys. 251, 272\u2013291 (2013)","journal-title":"J. Comput. Phys."},{"key":"807_CR24","doi-asserted-by":"crossref","unstructured":"Renac, F., de la Llave Plata, M., Martin, E., Chapelier, J.-B., Couaillier, V.: Aghora: a high-order DG solver for turbulent flow simulations. In: Kroll, N., Hirsch, C., Bassi, F., Johnston, C., Hillewaert, K. (eds.) IDIHOM: Industrialization of High-Order Methods\u2014A Top-Down Approach, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 128. Springer, New York (2015)","DOI":"10.2514\/6.2015-0058"},{"key":"807_CR25","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":"807_CR26","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1137\/S0036142901389025","volume":"40","author":"RJ Spiteri","year":"2002","unstructured":"Spiteri, R.J., Ruuth, S.J.: A new class of optimal high-order strong-stability-preserving time discretization methods. SIAM J. Numer. Anal. 40, 469\u2013491 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"807_CR27","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":"807_CR28","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":"807_CR29","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1007\/s00211-011-0443-7","volume":"121","author":"X Zhang","year":"2012","unstructured":"Zhang, X., Shu, C.-W.: A minimum entropy principle of high order schemes for gas dynamics equations. Numer. Math. 121, 545\u2013563 (2012)","journal-title":"Numer. Math."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-016-0807-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-016-0807-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-016-0807-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-016-0807-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T14:33:27Z","timestamp":1655735607000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-016-0807-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,7]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,2]]}},"alternative-id":["807"],"URL":"https:\/\/doi.org\/10.1007\/s00211-016-0807-0","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5,7]]}}}