{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:33:42Z","timestamp":1772292822329,"version":"3.50.1"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,11,16]],"date-time":"2015-11-16T00:00:00Z","timestamp":1447632000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2015,11,16]],"date-time":"2015-11-16T00:00:00Z","timestamp":1447632000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["ACI 1339801"],"award-info":[{"award-number":["ACI 1339801"]}],"id":[{"id":"10.13039\/100000001","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":[[2016,7]]},"DOI":"10.1007\/s10915-015-0133-1","type":"journal-article","created":{"date-parts":[[2015,11,16]],"date-time":"2015-11-16T14:38:41Z","timestamp":1447684721000},"page":"191-212","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Hybridized Discontinuous Galerkin Method for the Nonlinear Korteweg\u2013de Vries Equation"],"prefix":"10.1007","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6430-5266","authenticated-orcid":false,"given":"Ali","family":"Samii","sequence":"first","affiliation":[]},{"given":"Nishant","family":"Panda","sequence":"additional","affiliation":[]},{"given":"Craig","family":"Michoski","sequence":"additional","affiliation":[]},{"given":"Clint","family":"Dawson","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,11,16]]},"reference":[{"key":"133_CR1","unstructured":"Alexanderian, A., Petra, N., Stadler, G., Ghattas, O.: A fast and scalable method for a-optimal design of experiments for infinite-dimensional bayesian nonlinear inverse problems, p.\u00a029 (2014)"},{"issue":"4","key":"133_CR2","doi-asserted-by":"publisher","first-page":"371","DOI":"10.4171\/IFB\/130","volume":"7","author":"S Benzoni-Gavage","year":"2005","unstructured":"Benzoni-Gavage, S., Danchin, R., Descombes, S., Jamet, D.: Structure of Korteweg models and stability of diffuse interfaces. Interfaces Free Bound. 7(4), 371\u2013414 (2005)","journal-title":"Interfaces Free Bound."},{"key":"133_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-36519-5","volume-title":"Mixed Finite Element Methods and Applications","author":"D Boffi","year":"2013","unstructured":"Boffi, D., Brezzi, F., Fortin, M.: Mixed Finite Element Methods and Applications, vol. 44. Springer, Berlin (2013)"},{"key":"133_CR4","first-page":"205","volume":"1","author":"SI Braginskii","year":"1965","unstructured":"Braginskii, S.I.: Transport processes in a plasma. Rev. Plasma Phys. 1, 205 (1965)","journal-title":"Rev. Plasma Phys."},{"issue":"5, 1","key":"133_CR5","doi-asserted-by":"publisher","first-page":"2579","DOI":"10.1121\/1.420313","volume":"102","author":"M Buckingham","year":"1997","unstructured":"Buckingham, M.: Theory of acoustic attenuation, dispersion, and pulse propagation in unconsolidated granular materials including marine sediments. J. Acoust. Soc. Am. 102(5, 1), 2579\u20132596 (1997)","journal-title":"J. Acoust. Soc. Am."},{"issue":"1","key":"133_CR6","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1137\/S0036142902417893","volume":"42","author":"B Cockburn","year":"2004","unstructured":"Cockburn, B., Gopalakrishnan, J.: A characterization of hybridized mixed methods for second order elliptic problems. SIAM J. Numer. Anal. 42(1), 283\u2013301 (2004)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"133_CR7","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1137\/070706616","volume":"47","author":"B Cockburn","year":"2009","unstructured":"Cockburn, B., Gopalakrishnan, J., Lazarov, R.: Unified hybridization of discontinuous galerkin, mixed, and continuous galerkin methods for second order elliptic problems. SIAM J. Numer. Anal. 47(2), 1319\u20131365 (2009)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"133_CR8","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1137\/S0036139992240425","volume":"54","author":"CL Gardner","year":"1994","unstructured":"Gardner, C.L.: The quantum hydrodynamic model for semiconductor devices. SIAM J. Appl. Math. 54(2), 409\u2013427 (1994)","journal-title":"SIAM J. Appl. Math."},{"issue":"4","key":"133_CR9","doi-asserted-by":"publisher","first-page":"1140","DOI":"10.1016\/j.jcp.2011.09.020","volume":"231","author":"RE Heath","year":"2012","unstructured":"Heath, R.E., Gamba, I.M., Morrison, P.J., Michler, C.: A discontinuous Galerkin method for the Vlasov\u2013Poisson system. J. Comput. Phys. 231(4), 1140\u20131174 (2012)","journal-title":"J. Comput. Phys."},{"issue":"8","key":"133_CR10","doi-asserted-by":"publisher","first-page":"1151","DOI":"10.1080\/03605300600718503","volume":"31","author":"J Holmer","year":"2006","unstructured":"Holmer, J.: The initial-boundary value problem for the Korteweg\u2013de Vries equation. Commun. Partial Differ. Equ. 31(8), 1151\u20131190 (2006)","journal-title":"Commun. Partial Differ. Equ."},{"issue":"4","key":"133_CR11","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1080\/01495731003656998","volume":"33","author":"A Jain","year":"2010","unstructured":"Jain, A., Tamma, K.K.: Elliptic heat conduction specialized applications involving high gradients: local discontinuous galerkin finite element method\u2014part 1. J. Therm. Stresses 33(4), 335\u2013343 (2010)","journal-title":"J. Therm. Stresses"},{"key":"133_CR12","unstructured":"Kaladze, T., Aburjania, G., Kharshiladze, O., Horton, W., Kim, Y.: Theory of magnetized Rossby waves in the ionospheric E layer. J. Geophys. Res. Space Phys"},{"issue":"1","key":"133_CR13","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/s10915-011-9501-7","volume":"51","author":"RM Kirby","year":"2012","unstructured":"Kirby, R.M., Sherwin, S.J., Cockburn, B.: To CG or to HDG: a comparative study. J. Sci. Comput. 51(1), 183\u2013212 (2012)","journal-title":"J. Sci. Comput."},{"issue":"21","key":"133_CR14","doi-asserted-by":"publisher","first-page":"7863","DOI":"10.1016\/j.jcp.2009.06.041","volume":"228","author":"A Kloeckner","year":"2009","unstructured":"Kloeckner, A., Warburton, T., Bridge, J., Hesthaven, J.S.: Nodal discontinuous Galerkin methods on graphics processors. J. Comput. Phys. 228(21), 7863\u20137882 (2009)","journal-title":"J. Comput. Phys."},{"key":"133_CR15","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1080\/14786449508620739","volume":"39","author":"DJ Korteweg","year":"1895","unstructured":"Korteweg, D.J., de Vries, G.: On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves. Philos. Mag. 39, 422\u2013443 (1895)","journal-title":"Philos. Mag."},{"issue":"5","key":"133_CR16","doi-asserted-by":"publisher","first-page":"741","DOI":"10.1051\/m2an:2003042","volume":"37","author":"I Kostin","year":"2003","unstructured":"Kostin, I., Marion, M., Texier-Picard, R., Volpert, V.: Modelling of miscible liquids with the Korteweg stress. ESAIM-Math. Modell. Numer. Anal. 37(5), 741\u2013753 (2003)","journal-title":"ESAIM-Math. Modell. Numer. Anal."},{"issue":"1\u20133","key":"133_CR17","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/j.cma.2006.05.002","volume":"196","author":"EJ Kubatko","year":"2006","unstructured":"Kubatko, E.J., Westerink, J.J., Dawson, C.: hp discontinuous Galerkin methods for advection dominated problems in shallow water flow. Comput. Methods Appl. Mech. Eng. 196(1\u20133), 437\u2013451 (2006)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"133_CR18","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.physd.2013.10.006","volume":"266","author":"W Larecki","year":"2014","unstructured":"Larecki, W., Banach, Z.: Influence of nonlinearity of the phonon dispersion relation on wave velocities in the four-moment maximum entropy phonon hydrodynamics. Phys. D-Nonlinear Phenom. 266, 65\u201379 (2014)","journal-title":"Phys. D-Nonlinear Phenom."},{"issue":"2","key":"133_CR19","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1016\/j.jcp.2003.11.013","volume":"196","author":"D Levy","year":"2004","unstructured":"Levy, D., Shu, C.-W., Yan, J.: Local discontinuous Galerkin methods for nonlinear dispersive equations. J. Comput. Phys. 196(2), 751\u2013772 (2004)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"133_CR20","doi-asserted-by":"crossref","first-page":"240","DOI":"10.4208\/cicp.250509.210610a","volume":"9","author":"J Loverich","year":"2011","unstructured":"Loverich, J., Hakim, A., Shumlak, U.: A discontinuous Galerkin method for ideal two-fluid plasma equations. Commun. Comput. Phys. 9(2), 240\u2013268 (2011)","journal-title":"Commun. Comput. Phys."},{"issue":"23","key":"133_CR21","doi-asserted-by":"publisher","first-page":"8589","DOI":"10.1016\/j.jcp.2009.08.011","volume":"228","author":"C Michoski","year":"2009","unstructured":"Michoski, C., Evans, J.A., Schmitz, P.G., Vasseur, A.: Quantum hydrodynamics with trajectories: the nonlinear conservation form mixed\/discontinuous Galerkin method with applications in chemistry. J. Comput. Phys. 228(23), 8589\u20138608 (2009)","journal-title":"J. Comput. Phys."},{"key":"133_CR22","doi-asserted-by":"publisher","first-page":"898","DOI":"10.1016\/j.jcp.2014.06.058","volume":"274","author":"C Michoski","year":"2014","unstructured":"Michoski, C., Meyerson, D., Isaac, T., Waelbroeck, F.: Discontinuous galerkin methods for plasma physics in the scrape-off layer of tokamaks. J. Comput. Phys. 274, 898\u2013919 (2014)","journal-title":"J. Comput. Phys."},{"issue":"23","key":"133_CR23","doi-asserted-by":"publisher","first-page":"8841","DOI":"10.1016\/j.jcp.2009.08.030","volume":"228","author":"NC Nguyen","year":"2009","unstructured":"Nguyen, N.C., Peraire, J., Cockburn, B.: An implicit high-order hybridizable discontinuous galerkin method for nonlinear convection\u2013diffusion equations. J. Comput. Phys. 228(23), 8841\u20138855 (2009)","journal-title":"J. Comput. Phys."},{"key":"133_CR24","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1016\/j.jcp.2014.05.035","volume":"273","author":"N Panda","year":"2014","unstructured":"Panda, N., Dawson, C., Zhang, Y., Kennedy, A.B., Westerink, J.J., Donahue, A.S.: Discontinuous Galerkin methods for solving Boussinesq\u2013Green\u2013Naghdi equations in resolving non-linear and dispersive surface water waves. J. Comput. Phys. 273, 572\u2013588 (2014)","journal-title":"J. Comput. Phys."},{"key":"133_CR25","first-page":"2010","volume":"363","author":"J Peraire","year":"2010","unstructured":"Peraire, J., Nguyen, N., Cockburn, B.: A hybridizable discontinuous Galerkin method for the compressible Euler and Navier\u2013Stokes equations. AIAA Pap. 363, 2010 (2010)","journal-title":"AIAA Pap."},{"key":"133_CR26","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1146\/annurev.fl.06.010174.000521","volume":"6","author":"O Phillips","year":"1974","unstructured":"Phillips, O.: Nonlinear dispersive waves. Annu. Rev. Fluid Mech. 6, 93\u2013110 (1974)","journal-title":"Annu. Rev. Fluid Mech."},{"issue":"3","key":"133_CR27","doi-asserted-by":"publisher","first-page":"885","DOI":"10.1103\/RevModPhys.83.885","volume":"83","author":"PK Shukla","year":"2011","unstructured":"Shukla, P.K., Eliasson, B.: Colloquium: nonlinear collective interactions in quantum plasmas with degenerate electron fluids. Rev. Mod. Phys. 83(3), 885\u2013906 (2011)","journal-title":"Rev. Mod. Phys."},{"key":"133_CR28","doi-asserted-by":"crossref","unstructured":"Tassi, E., Morrison, P.J., Waelbroeck, F.L., Grasso, D.: Hamiltonian formulation and analysis of a collisionless fluid reconnection model. Plasma Phys. Control. Fusion 50(8), 085014 (2008)","DOI":"10.1088\/0741-3335\/50\/8\/085014"},{"key":"133_CR29","unstructured":"Woo, S.-B., Choi, Y.-K.: Development of finite volume model for KDV type equation. In: Zuo, Q.H., Dou, X.P., Ge, J.F., (Eds.), Asian and pacific coasts 2007, pp. 203\u2013206, 2007. In: 4th International Conference on Asian and Pacific Coasts, Nanjing Hydraul Res Inst, Nanjing, Peoples Republic of China, Sept 21\u201324 (2007)"},{"issue":"7","key":"133_CR30","doi-asserted-by":"publisher","first-page":"2135","DOI":"10.1063\/1.870611","volume":"1","author":"M Yagi","year":"1994","unstructured":"Yagi, M., Horton, W.: Reduced Braginskii equations. Phys. Plasmas 1(7), 2135\u20132139 (1994)","journal-title":"Phys. Plasmas"},{"issue":"2","key":"133_CR31","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1137\/S0036142901390378","volume":"40","author":"J Yan","year":"2002","unstructured":"Yan, J., Shu, C.: A local discontinuous Galerkin method for KdV type equations. SIAM J. Numer. Anal. 40(2), 769\u2013791 (2002)","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"133_CR32","doi-asserted-by":"publisher","first-page":"537","DOI":"10.3846\/13926292.2014.960016","volume":"19","author":"W Yan","year":"2014","unstructured":"Yan, W., Liu, Z., Liang, Y.: Existence of solitary waves and periodic waves to a perturbed generalized KdV equation. Math. Model. Anal. 19(4), 537\u2013555 (2014)","journal-title":"Math. Model. Anal."},{"key":"133_CR33","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/j.coastaleng.2012.09.005","volume":"73","author":"Y Zhang","year":"2013","unstructured":"Zhang, Y., Kennedy, A.B., Panda, N., Dawson, C., Westerink, J.J.: Boussinesq\u2013Green\u2013Naghdi rotational water wave theory. Coast. Eng. 73, 13\u201327 (2013)","journal-title":"Coast. Eng."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-015-0133-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-015-0133-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-015-0133-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-015-0133-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T09:16:24Z","timestamp":1589706984000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-015-0133-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,16]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,7]]}},"alternative-id":["133"],"URL":"https:\/\/doi.org\/10.1007\/s10915-015-0133-1","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,16]]},"assertion":[{"value":"8 January 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 November 2015","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 November 2015","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 November 2015","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}