{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T09:10:21Z","timestamp":1790673021894,"version":"4.1.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,1,3]],"date-time":"2019-01-03T00:00:00Z","timestamp":1546473600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91630205"],"award-info":[{"award-number":["91630205"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771068"],"award-info":[{"award-number":["11771068"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11501062"],"award-info":[{"award-number":["11501062"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871139"],"award-info":[{"award-number":["11871139"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11701055"],"award-info":[{"award-number":["11701055"]}],"id":[{"id":"10.13039\/501100001809","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":[[2019,6]]},"DOI":"10.1007\/s10915-018-00895-x","type":"journal-article","created":{"date-parts":[[2019,1,3]],"date-time":"2019-01-03T11:57:28Z","timestamp":1546516648000},"page":"1361-1388","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Maximum-Principle-Satisfying and Positivity-Preserving High Order Central DG Methods on Unstructured Overlapping Meshes for Two-Dimensional Hyperbolic Conservation Laws"],"prefix":"10.1007","volume":"79","author":[{"given":"Maojun","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haiyun","family":"Dong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Binbin","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liwei","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,1,3]]},"reference":[{"key":"895_CR1","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1006\/jcph.2000.6666","volume":"167","author":"M Brio","year":"2001","unstructured":"Brio, M., Zakharian, A.R., Webb, G.M.: Two-dimensional Riemann solver for Euler equations of gas dynamics. J. Comput. Phys. 167, 177\u2013195 (2001)","journal-title":"J. Comput. Phys."},{"key":"895_CR2","doi-asserted-by":"publisher","first-page":"77","DOI":"10.4208\/aamm.2016.m1182","volume":"10","author":"G Chen","year":"2018","unstructured":"Chen, G., Feng, M.: Stabilized finite element methods for the Biot\u2019s consolidation problem. Adv. Appl. Math. Mech. 10, 77\u201399 (2018)","journal-title":"Adv. Appl. Math. Mech."},{"key":"895_CR3","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1016\/j.cam.2018.05.028","volume":"343","author":"G Chen","year":"2018","unstructured":"Chen, G., Hu, W.W., Shen, J.G., Singler, J.R., Zhang, Y.W., Zheng, X.B.: An HDG method for distributed control of convection diffusion PDEs. J. Comput. Appl. Math. 343, 643\u2013661 (2018)","journal-title":"J. Comput. Appl. Math."},{"key":"895_CR4","doi-asserted-by":"crossref","first-page":"9043","DOI":"10.1016\/j.amc.2013.03.104","volume":"219","author":"Y Chen","year":"2013","unstructured":"Chen, Y., Luo, Y., Feng, M.: Analysis of a discontinuous Galerkin method for the Biot\u2019s consolidation problem. Appl. Math. Comput. 219, 9043\u20139056 (2013)","journal-title":"Appl. Math. Comput."},{"key":"895_CR5","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/j.jcp.2012.12.019","volume":"238","author":"Y Cheng","year":"2013","unstructured":"Cheng, Y., Li, F., Qiu, J., Xu, L.: Positivity-preserving DG and central DG methods for ideal MHD equations. J. Comput. Phys. 238, 255\u2013280 (2013)","journal-title":"J. Comput. Phys."},{"key":"895_CR6","doi-asserted-by":"publisher","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":"895_CR7","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1006\/jcph.1998.5892","volume":"141","author":"B Cockburn","year":"1998","unstructured":"Cockburn, B., Shu, C.-W.: The Runge\u2013Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. Comput. Phys. 141, 199\u2013224 (1998)","journal-title":"J. Comput. Phys."},{"key":"895_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22019-1","volume-title":"Hyperbolic Conservation Laws in Continuum Physics","author":"CM Dafermos","year":"2000","unstructured":"Dafermos, C.M.: Hyperbolic Conservation Laws in Continuum Physics. Springer, Berlin (2000)"},{"key":"895_CR9","doi-asserted-by":"publisher","first-page":"1347","DOI":"10.1007\/s10915-017-0511-y","volume":"74","author":"X-L Deng","year":"2018","unstructured":"Deng, X.-L., Li, M.: Simulating compressible two-medium flows with sharp-interface adaptive Runge\u2013Kutta discontinuous Galerkin methods. J. Sci. Comput. 74, 1347\u20131368 (2018)","journal-title":"J. Sci. Comput."},{"key":"895_CR10","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.apnum.2016.08.008","volume":"110","author":"H Dong","year":"2016","unstructured":"Dong, H., Li, M.: A reconstructed central discontinuous Galerkin-finite element method for the fully nonlinear weakly dispersive Green\u2013Naghdi model. Appl. Numer. Math. 110, 110\u2013127 (2016)","journal-title":"Appl. Numer. Math."},{"key":"895_CR11","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.compfluid.2017.05.011","volume":"153","author":"H Dong","year":"2017","unstructured":"Dong, H., Lv, M., Li, M.: A reconstructed central discontinuous Galerkin method for conservation laws. Comput. Fluids 153, 76\u201384 (2017)","journal-title":"Comput. Fluids"},{"key":"895_CR12","doi-asserted-by":"publisher","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":"895_CR13","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1006\/jcph.1996.0130","volume":"126","author":"G-S Jiang","year":"1996","unstructured":"Jiang, G.-S., Shu, C.-W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202\u2013228 (1996)","journal-title":"J. Comput. Phys."},{"key":"895_CR14","doi-asserted-by":"publisher","first-page":"3327","DOI":"10.1137\/120896037","volume":"51","author":"HH Kim","year":"2013","unstructured":"Kim, H.H., Chung, E.T., Lee, C.S.: A staggered discontinuous Galerkin method for the Stokes system. SIAM J. Numer. Anal. 51, 3327\u20133350 (2013)","journal-title":"SIAM J. Numer. Anal."},{"key":"895_CR15","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1007\/s10915-009-9340-y","volume":"45","author":"F Li","year":"2010","unstructured":"Li, F., Yakovlev, S.: A central discontinuous Galerkin method for Hamilton\u2013Jacobi equations. J. Sci. Comput. 45, 404\u2013428 (2010)","journal-title":"J. Sci. Comput."},{"key":"895_CR16","doi-asserted-by":"publisher","first-page":"2655","DOI":"10.1016\/j.jcp.2011.12.016","volume":"231","author":"F Li","year":"2012","unstructured":"Li, F., Xu, L.: Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations. J. Comput. Phys. 231, 2655\u20132675 (2012)","journal-title":"J. Comput. Phys."},{"key":"895_CR17","doi-asserted-by":"publisher","first-page":"4828","DOI":"10.1016\/j.jcp.2011.03.006","volume":"230","author":"F Li","year":"2011","unstructured":"Li, F., Xu, L., Yakovlev, S.: Central discontinuous Galerkin methods for ideal MHD equations with exactly divergence-free magnetic field. J. Comput. Phys. 230, 4828\u20134847 (2011)","journal-title":"J. Comput. Phys."},{"key":"895_CR18","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.jcp.2013.09.050","volume":"257","author":"M Li","year":"2014","unstructured":"Li, M., Guyenne, P., Li, F., Xu, L.: High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model. J. Comput. Phys. 257, 169\u2013192 (2014)","journal-title":"J. Comput. Phys."},{"key":"895_CR19","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.amc.2013.11.016","volume":"227","author":"M Li","year":"2014","unstructured":"Li, M., Chen, A.: High order central discontinuous Galerkin-finite element methods for the Camassa\u2013Holm equation. Appl. Math. Comput. 227, 237\u2013245 (2014)","journal-title":"Appl. Math. Comput."},{"key":"895_CR20","doi-asserted-by":"publisher","first-page":"A3720","DOI":"10.1137\/16M1070001","volume":"38","author":"M Li","year":"2016","unstructured":"Li, M., Li, F.Z., Xu, L.: Maximum-principle-satisfying and positivity-preserving high order CDG methods for conservation laws. SIAM J. Sci. Comput. 38, A3720\u2013A3740 (2016)","journal-title":"SIAM J. Sci. Comput."},{"key":"895_CR21","doi-asserted-by":"publisher","first-page":"994","DOI":"10.1007\/s10915-016-0329-z","volume":"711","author":"M Li","year":"2017","unstructured":"Li, M., Guyenne, P., Li, F., Xu, L.: A positivity-preserving well-balanced central discontinuous Galerkin method for the nonlinear shallow water equations. J. Sci. Comput. 711, 994\u20131034 (2017)","journal-title":"J. Sci. Comput."},{"key":"895_CR22","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.amc.2017.07.050","volume":"315","author":"M Li","year":"2017","unstructured":"Li, M., Jiang, Y., Dong, H.: High order well-balanced central local discontinuous Galerkin-finite element methods for solving the Green\u2013Naghdi model. Appl. Math. Comput. 315, 113\u2013130 (2017)","journal-title":"Appl. Math. Comput."},{"key":"895_CR23","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1002\/mma.3477","volume":"39","author":"X Li","year":"2016","unstructured":"Li, X.: Boundedness in a two-dimensional attraction-repulsion system with nonlinear diffusion. Math. Methods Appl. Sci. 39, 289\u2013301 (2016)","journal-title":"Math. Methods Appl. Sci."},{"key":"895_CR24","doi-asserted-by":"publisher","first-page":"2442","DOI":"10.1137\/060666974","volume":"45","author":"Y Liu","year":"2007","unstructured":"Liu, Y., Shu, C.-W., Tadmor, E., Zhang, M.: Central discontinuous Galerkin methods on overlapping cells with a nonoscillatary hierarchical reconstruction. SIAM J. Numer. Anal. 45, 2442\u20132467 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"895_CR25","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.1051\/m2an\/2011007","volume":"45","author":"Y Liu","year":"2011","unstructured":"Liu, Y., Shu, C.-W., Tadmor, E., Zhang, M.: Central local discontinuous Galerkin methods on overlapping cells for diffusion equations. ESAIM: Math. Model. Numer. Anal. 45, 1009\u20131032 (2011)","journal-title":"ESAIM: Math. Model. Numer. Anal."},{"key":"895_CR26","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1186\/1687-2770-2011-48","volume":"2011","author":"Y Luo","year":"2011","unstructured":"Luo, Y., Feng, M., Xu, Y.: A stabilized mixed discontinuous Galerkin method for the incompressible miscible displacement problem. Bound. Value Probl. 2011, 48 (2011)","journal-title":"Bound. Value Probl."},{"key":"895_CR27","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 (1973)"},{"key":"895_CR28","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1016\/j.jfa.2014.04.020","volume":"267","author":"X Ren","year":"2014","unstructured":"Ren, X., Wu, J., Xiang, Z., Zhang, Z.: Global existence and decay of smooth solution for the 2-D MHD equation without magnetic diffusion. J. Funct. Anal. 267, 503\u2013541 (2014)","journal-title":"J. Funct. Anal."},{"key":"895_CR29","volume-title":"Essentially Non-oscillatory and Weighted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws, ICASE Report","author":"C-W Shu","year":"1997","unstructured":"Shu, C.-W.: Essentially Non-oscillatory and Weighted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws, ICASE Report. Brown University, Rhode Island (1997)"},{"key":"895_CR30","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1007\/s001930050083","volume":"7","author":"M Sun","year":"1997","unstructured":"Sun, M., Takayama, K.: The formation of a secondary shock wave behind a shock wave diffracting at a convex corner. Shock Waves 7, 287\u2013295 (1997)","journal-title":"Shock Waves"},{"key":"895_CR31","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1016\/j.compfluid.2004.01.004","volume":"34","author":"H Tang","year":"2005","unstructured":"Tang, H., Warnecke, G.: A Runge\u2013Kutta discontinuous Galerkin method for the Euler equations. Comput. Fluids 34, 375\u2013398 (2005)","journal-title":"Comput. Fluids"},{"key":"895_CR32","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1006\/jcph.2002.7076","volume":"179","author":"S Vukovic","year":"2002","unstructured":"Vukovic, S., Sopta, L.: ENO and WENO schemes with the exact conservation property for one-dimensional shallow water equations. J. Comput. Phys. 179, 593\u2013621 (2002)","journal-title":"J. Comput. Phys."},{"key":"895_CR33","doi-asserted-by":"publisher","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":"895_CR34","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.jcp.2016.09.044","volume":"327","author":"Z Xu","year":"2016","unstructured":"Xu, Z., Liu, Y.: New central and central discontinuous Galerkin schemes on overlapping cells of unstructured grids for solving ideal magnetohydrodynamic equations with globally divergence-free magnetic field. J. Comput. Phys. 327, 203\u2013224 (2016)","journal-title":"J. Comput. Phys."},{"key":"895_CR35","doi-asserted-by":"publisher","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":"895_CR36","doi-asserted-by":"publisher","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":"895_CR37","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s10915-011-9472-8","volume":"50","author":"X Zhang","year":"2012","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. Sci. Comput. 50, 29\u201362 (2012)","journal-title":"J. Sci. Comput."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-00895-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-018-00895-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-00895-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,9]],"date-time":"2022-09-09T17:01:26Z","timestamp":1662742886000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-018-00895-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,3]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["895"],"URL":"https:\/\/doi.org\/10.1007\/s10915-018-00895-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,3]]},"assertion":[{"value":"29 July 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 November 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 December 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 January 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}