{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T10:33:27Z","timestamp":1758710007163,"version":"3.37.3"},"reference-count":58,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,5,26]],"date-time":"2017-05-26T00:00:00Z","timestamp":1495756800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,1]]},"DOI":"10.1007\/s10915-017-0455-2","type":"journal-article","created":{"date-parts":[[2017,5,26]],"date-time":"2017-05-26T13:50:54Z","timestamp":1495806654000},"page":"491-518","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["High Order $$C^0$$ C 0 -Continuous Galerkin Schemes for High Order PDEs, Conservation of Quadratic Invariants and Application to the Korteweg-de Vries Model"],"prefix":"10.1007","volume":"74","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5976-4847","authenticated-orcid":false,"given":"Sebastian","family":"Minjeaud","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Richard","family":"Pasquetti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,5,26]]},"reference":[{"key":"455_CR1","doi-asserted-by":"crossref","first-page":"1256","DOI":"10.1016\/j.amc.2005.08.038","volume":"175","author":"EN Aksan","year":"2006","unstructured":"Aksan, E.N., \u00d6zdes, A.: Numerical solution of the Korteweg-de Vries equation by Galerkin B-spline finite element method. Appl. Math. Comput. 175, 1256\u20131265 (2006)","journal-title":"Appl. Math. Comput."},{"key":"455_CR2","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1137\/0732037","volume":"32","author":"UM Ascher","year":"1995","unstructured":"Ascher, U.M., Ruth, S.J., Wetton, B.: Implicit\u2013explicit methods for time-dependent PDE\u2019s. SIAM J. Numer. Anal. 32, 797\u2013823 (1995)","journal-title":"SIAM J. Numer. Anal."},{"key":"455_CR3","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/S0168-9274(97)00056-1","volume":"25","author":"UM Ascher","year":"1997","unstructured":"Ascher, U.M., Ruth, S.J., Spiteri, R.J.: Implicit\u2013explicit Runge\u2013Kutta methods for time-dependent partial differential equations. Appl. Num. Math. 25, 151\u2013167 (1997)","journal-title":"Appl. Num. Math."},{"issue":"163","key":"455_CR4","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1090\/S0025-5718-1983-0689464-4","volume":"40","author":"GA Baker","year":"1983","unstructured":"Baker, G.A., Dougalis, V.A., Karakashian, O.A.: Convergence of Galerkin approximations for the Korteweg-de Vries equation. Math. Comput. 40(163), 419\u2013433 (1983)","journal-title":"Math. Comput."},{"issue":"5","key":"455_CR5","first-page":"1049","volume":"24","author":"YU Berezin","year":"1967","unstructured":"Berezin, Y.U., Karpman, V.I.: Nonlinear evolution of disturbances in plasmas and other dispersive media. Sov. Phys. Jetp 24(5), 1049\u20131055 (1967)","journal-title":"Sov. Phys. Jetp"},{"key":"455_CR6","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1098\/rsta.1995.0027","volume":"351","author":"JL Bona","year":"1995","unstructured":"Bona, J.L., Dougalis, V.A., Karakashian, O.A., McKinney, W.R.: Conservative high-order numerical schemes for the generalized Korteweg-de Vries equation. Phil. Trans. R. Soc. Lond. 351, 107\u2013164 (1995)","journal-title":"Phil. Trans. R. Soc. Lond."},{"issue":"283","key":"455_CR7","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.1090\/S0025-5718-2013-02661-0","volume":"82","author":"JL Bona","year":"2013","unstructured":"Bona, J.L., Chen, H., Karakashian, O., Xing, Y.: Conservative, discontinuous Galerkin methods for the generalized Korteweg-de Vries equation. Math. Comput. 82(283), 1401\u20131432 (2013)","journal-title":"Math. Comput."},{"key":"455_CR8","first-page":"247","volume":"20","author":"ND Bueno","year":"1996","unstructured":"Bueno, N.D., Mastroserio, C.: Explicit methods based on a class of four stage fourth order Runge\u2013Kutta methods for preserving quadratic invariants. J. of Comput. Appl. Math. 20, 247\u2013260 (1996)","journal-title":"J. of Comput. Appl. Math."},{"key":"455_CR9","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/S0168-9274(97)00056-1","volume":"25","author":"JC Butcher","year":"1997","unstructured":"Butcher, J.C.: A histoty of Runge\u2013Kutta methods. Appl. Num. Math. 25, 151\u2013167 (1997)","journal-title":"Appl. Num. Math."},{"issue":"3","key":"455_CR10","doi-asserted-by":"crossref","first-page":"868885","DOI":"10.1137\/04061979X","volume":"28","author":"M Calvo","year":"2006","unstructured":"Calvo, M., Hern\u00e1ndez-Abreu, D., Montijano, J.I., R\u00e1ndez, L.: On the preservation of invariants by explicit Runge\u2013Kutta methods. SIAM J. Sci. Comput. 28(3), 868885 (2006)","journal-title":"SIAM J. Sci. Comput."},{"key":"455_CR11","doi-asserted-by":"crossref","first-page":"231251","DOI":"10.1007\/s10444-014-9355-2","volume":"41","author":"M Calvo","year":"2015","unstructured":"Calvo, M., Laburta, M.P., Montijano, J.I., R\u00e1ndez, L.: Runge\u2013Kutta. Adv. Comput. Math. 41, 231251 (2015)","journal-title":"Adv. Comput. Math."},{"key":"455_CR12","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.cpc.2015.02.008","volume":"192","author":"CD Cantwell","year":"2015","unstructured":"Cantwell, C.D., Moxey, D., Comerford, A., Bolis, A., Rocco, G., Mengaldo, G., De Grazia, D., Yakovlev, S., Lombard, J.-E., Ekelschot, D., Jordi, B., Xu, H., Mohamied, Y., Eskilsson, C., Nelson, B., Vos, P., Biotto, C., Kirby, R.M., Sherwin, S.J.: Nektar++: an open-source spectral\/hp element framework. Comput. Phys. Commun. 192, 205\u2013219 (2015)","journal-title":"Comput. Phys. Commun."},{"key":"455_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-30728-0","volume-title":"Spectral Methods, Evolution to Complex Geometries and Applications to Fluid Dynamics","author":"C Canuto","year":"2007","unstructured":"Canuto, C., Hussaini, M., Quarteroni, A., Zang, T.: Spectral Methods, Evolution to Complex Geometries and Applications to Fluid Dynamics. Springer Verlag, Berlin (2007)"},{"key":"455_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0045-7825(91)90112-J","volume":"93","author":"GF Carey","year":"1991","unstructured":"Carey, G.F., Shen, Y.: Approximation of the KdV equation by least square finite elements. J. Comput. Methods Appl. Mech. Eng. 93, 1\u201311 (1991)","journal-title":"J. Comput. Methods Appl. Mech. Eng."},{"key":"455_CR15","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1051\/m2an\/2009020","volume":"43","author":"E Celledoni","year":"2009","unstructured":"Celledoni, E., McLachlan, R.I., McLaren, D.I., Owen, B., Quispel, G.R.W., Wright, W.M.: Energy-preserving Runge\u2013Kutta methods. ESAIM: M2AN 43, 645\u2013649 (2009)","journal-title":"ESAIM: M2AN"},{"key":"455_CR16","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1002\/(SICI)1098-2426(199801)14:1<63::AID-NUM4>3.0.CO;2-J","volume":"14","author":"G Cohen","year":"1998","unstructured":"Cohen, G., Monk, P.: Gauss point mass lumping schemes for Maxwell\u2019s equations. Numer. Methods Partial Differ. Equ. 14, 63\u201388 (1998)","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"1","key":"455_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/imanum\/7.1.1","volume":"7","author":"GJ Cooper","year":"1987","unstructured":"Cooper, G.J.: Stability of Runge\u2013Kutta methods for trajectory problems. IMA J. Numer. Anal. 7(1), 1\u201313 (1987)","journal-title":"IMA J. Numer. Anal."},{"issue":"1","key":"455_CR18","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/j.jcp.2007.07.031","volume":"227","author":"Y Cui","year":"2007","unstructured":"Cui, Y., Mao, D.K.: Numerical method satisfying the first two conservation laws for the Korteweg-de Vries equation. J. Comput. Phys. 227(1), 376\u2013399 (2007)","journal-title":"J. Comput. Phys."},{"key":"455_CR19","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511546792","volume-title":"High-order methods for incompressible fluid flow","author":"MO Deville","year":"2002","unstructured":"Deville, M.O., Fischer, P.F., Mund, E.H.: High-order methods for incompressible fluid flow. Cambridge University Press, New York (2002)"},{"issue":"1","key":"455_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1025677921253","volume":"14","author":"Y Dubois-Pelerin","year":"1999","unstructured":"Dubois-Pelerin, Y., van Kemenade, V., Deville, M.: An object-oriented toolbox for spectral element analysis. J. Sci. Comput. 14(1), 1\u201329 (1999)","journal-title":"J. Sci. Comput."},{"key":"455_CR21","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1002\/fld.3681","volume":"71","author":"D Dutykh","year":"2013","unstructured":"Dutykh, D., Katsaounis, T., Mitsotakis, D.: Finite volume methods for unidirectional dispersive wave models. Int. J. Numer. Methods Fluids 71, 717\u2013736 (2013)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"455_CR22","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1016\/j.amc.2015.06.052","volume":"272","author":"M Dumbser","year":"2016","unstructured":"Dumbser, M., Facchini, M.: A space-time discontinuous Galerkin method for Boussinesq-type equations. Appl. Math. Comput. 272, 336\u2013346 (2016)","journal-title":"Appl. Math. Comput."},{"key":"455_CR23","unstructured":"Fischer, P. F., Lottes, J. W., Kerkemeier, S. G.: nek5000 Web page, http:\/\/nek5000.mcs.anl.gov , (2008)"},{"key":"455_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-59185-3","volume-title":"Spectral Elements for Transport-Dominated Equations","author":"D Funaro","year":"1997","unstructured":"Funaro, D.: Spectral Elements for Transport-Dominated Equations. Springer-Verlag, Berlin (1997)"},{"key":"455_CR25","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/0045-7825(91)90241-W","volume":"92","author":"LRT Gardner","year":"1991","unstructured":"Gardner, L.R.T., Gardner, G.A., Ali, A.H.A.: Simulations of solitons using quadratic spline finite elements. J. Comput. Methods Appl. Mech. Eng. 92, 231\u2013243 (1991)","journal-title":"J. Comput. Methods Appl. Mech. Eng."},{"issue":"11","key":"455_CR26","doi-asserted-by":"crossref","first-page":"4248","DOI":"10.1016\/j.jcp.2010.11.043","volume":"230","author":"JL Guermond","year":"2011","unstructured":"Guermond, J.L., Pasquetti, R., Popov, B.: Entropy viscosity method for non-linear conservation laws. J. Comput. Phys. 230(11), 4248\u20134267 (2011)","journal-title":"J. Comput. Phys."},{"key":"455_CR27","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1006\/jcph.1999.6273","volume":"153","author":"H Holden","year":"1999","unstructured":"Holden, H., Karlsen, K.H., Risebro, N.H.: Operator splitting methods for generalized Korteweg-de Vries equations. J. Comput. Phys. 153, 203\u2013222 (1999)","journal-title":"J. Comput. Phys."},{"key":"455_CR28","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0045-7825(98)00079-6","volume":"166","author":"TJR Hugues","year":"1998","unstructured":"Hugues, T.J.R., Feijoo, G.R., Mazzei, L., Quincy, J.B.: The variational multiscale method\u2014a paradigm for computational mechanics. Comput. Methods Appl. Mech. Eng. 166, 3\u201324 (1998)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"455_CR29","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/S0377-0427(00)00459-3","volume":"125","author":"A Iserles","year":"2000","unstructured":"Iserles, A., Zanna, A.: Preserving algebraic invariants with Runge\u2013Kutta methods. J. of Comput. Appl. Math. 125, 69\u201381 (2000)","journal-title":"J. of Comput. Appl. Math."},{"key":"455_CR30","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1215\/S0012-7094-06-13524-X","volume":"135","author":"T Kappeler","year":"2006","unstructured":"Kappeler, T., Topalov, P.: Global wellposedness of KdV in $$H^{-1} ({\\mathbb{T}}, {\\mathbb{R}})$$ H - 1 ( T , R ) . Duke Math. J. 135, 327\u2013360 (2006)","journal-title":"Duke Math. J."},{"key":"455_CR31","volume-title":"Spectral Hp Element Methods for CFD","author":"GE Karniadakis","year":"1999","unstructured":"Karniadakis, G.E., Sherwin, S.J.: Spectral Hp Element Methods for CFD. Oxford University Press, London (1999)"},{"key":"455_CR32","doi-asserted-by":"crossref","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, 183\u2013212 (2012)","journal-title":"J. Sci. Comput."},{"key":"455_CR33","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0021-9991(03)00314-0","volume":"191","author":"RM Kirby","year":"2003","unstructured":"Kirby, R.M., Karniadakis, G.E.: De-aliasing on non uniform grids: algorithms and applications. J. Comput. Phys. 191, 249\u2013264 (2003)","journal-title":"J. Comput. Phys."},{"issue":"10","key":"455_CR34","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1016\/0375-9601(67)90953-X","volume":"25A","author":"VI Karpman","year":"1967","unstructured":"Karpman, V.I.: An asymptotic solution of the Korteweg-de Vries equation. Phys. Lett. 25A(10), 708\u2013709 (1967)","journal-title":"Phys. Lett."},{"key":"455_CR35","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1002\/cpa.3160360302","volume":"XXXVI","author":"PD Lax","year":"1983","unstructured":"Lax, P.D., Levermore, C.D.: The small dispersion limit of the Korteweg-de Vries equation. I. Comm. Pure Appl. Math. XXXVI, 253\u2013290 (1983)","journal-title":"Comm. Pure Appl. Math."},{"key":"455_CR36","doi-asserted-by":"crossref","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, 751\u2013772 (2004)","journal-title":"J. Comput. Phys."},{"key":"455_CR37","first-page":"71","volume-title":"State-of-the-Art Surveys in Computational Mechanics","author":"Y Maday","year":"1989","unstructured":"Maday, Y., Patera, A.T.: Spectral element methods for the incompressible Navier\u2013Stokes equations. In: Noor, A.K. (ed.) State-of-the-Art Surveys in Computational Mechanics, pp. 71\u2013143. ASME, New York (1989)"},{"issue":"2","key":"455_CR38","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1137\/0730016","volume":"30","author":"Y Maday","year":"1993","unstructured":"Maday, Y., Kaber, S.M.O., Tadmor, E.: Legendre pseudo-spectral viscosity method for nonlinear conservation laws. SIAM J. Numer. Anal. 30(2), 321\u2013342 (1993)","journal-title":"SIAM J. Numer. Anal."},{"key":"455_CR39","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1017\/S0022112081001559","volume":"106","author":"JW Miles","year":"1984","unstructured":"Miles, J.W.: The Korteweg-de Vries equation: a historical essay. J. Fluid Mech. 106, 131\u2013147 (1984)","journal-title":"J. Fluid Mech."},{"key":"455_CR40","series-title":"Lecture Notes in Computational Science and Engineering","volume-title":"Stabilization of the Spectral Element Method in Turbulent Flow Simulations","author":"JP Ohlsson","year":"2011","unstructured":"Ohlsson, J.P., Schlatter, P., Fischer, P.F., Henningson, D.S.: Stabilization of the Spectral Element Method in Turbulent Flow Simulations. Lecture Notes in Computational Science and Engineering, vol. 76. Springer-Verlag, Berlin Heidelberg (2011)"},{"key":"455_CR41","volume-title":"Implicit\u2013Explicit Runge\u2013Kutta Schemes for Stiff Systems of Differential Equations, Recent trends in numerical analysis, 269\u2013288","author":"L Pareschi","year":"2000","unstructured":"Pareschi, L., Russo, G.: Implicit\u2013Explicit Runge\u2013Kutta Schemes for Stiff Systems of Differential Equations, Recent trends in numerical analysis, 269\u2013288. Nova Science Publishers, Inc., Commack (2000)"},{"key":"455_CR42","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s10915-015-0133-1","volume":"68","author":"A Samii","year":"2016","unstructured":"Samii, A., Panda, N., Michoski, C., Dawson, C.: A hybridized discontinuous Galerkin method for the nonlinear Korteweg-de Vries equation. J. Sci. Comput. 68, 191\u2013212 (2016)","journal-title":"J. Sci. Comput."},{"key":"455_CR43","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/0021-9991(81)90138-8","volume":"39","author":"JM Sanz-Serna","year":"1981","unstructured":"Sanz-Serna, J.M., Christie, I.: Petrov-Galerkin methods for nonlinear dispersive waves. J. Comput. Phys. 39, 94\u2013102 (1981)","journal-title":"J. Comput. Phys."},{"key":"455_CR44","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0021-9991(82)90074-2","volume":"47","author":"JM Sanz-Serna","year":"1982","unstructured":"Sanz-Serna, J.M.: An explicit finite-difference scheme with exact conservation properties. J. Comput. Phys. 47, 199\u2013210 (1982)","journal-title":"J. Comput. Phys."},{"issue":"5","key":"455_CR45","doi-asserted-by":"crossref","first-page":"1595","DOI":"10.1137\/S0036142902410271","volume":"41","author":"J Shen","year":"2003","unstructured":"Shen, J.: A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: application to the KdV equation. SIAM J. Numer. Anal. 41(5), 1595\u20131619 (2003)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"455_CR46","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1137\/0726003","volume":"26","author":"E Tadmor","year":"1989","unstructured":"Tadmor, E.: Convergence of spectral methods for nonlinear conservation laws. SIAM J. Numer. Anal. 26(1), 30\u201344 (1989)","journal-title":"SIAM J. Numer. Anal."},{"key":"455_CR47","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/0021-9991(84)90004-4","volume":"55","author":"TR Taha","year":"1984","unstructured":"Taha, T.R., Ablowitz, M.J.: Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation. J. Comput. Phys. 55, 231\u2013253 (1984)","journal-title":"J. Comput. Phys."},{"key":"455_CR48","doi-asserted-by":"crossref","first-page":"5161","DOI":"10.1016\/j.jcp.2010.03.031","volume":"229","author":"PEJ Vos","year":"2010","unstructured":"Vos, P.E.J., Sherwin, S.J., Kirby, R.M.: From $$h$$ h to $$p$$ p efficiently: implementing finite and spectral \/ $$hp$$ h p element methods to achieve optimal performance for low- and high-order discretisations. J. Comput. Phys. 229, 5161\u20135181 (2010)","journal-title":"J. Comput. Phys."},{"key":"455_CR49","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1002\/(SICI)1097-0363(19990130)29:2<143::AID-FLD779>3.0.CO;2-5","volume":"29","author":"M Walkley","year":"1999","unstructured":"Walkley, M., Berzins, M.: A finite element method for the one-dimensional extended Boussinesq equations. Int. J. Numer. Meth. Fluids 29, 143\u2013157 (1999)","journal-title":"Int. J. Numer. Meth. Fluids"},{"issue":"149","key":"455_CR50","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1090\/S0025-5718-1980-0551289-5","volume":"34","author":"R Winther","year":"1980","unstructured":"Winther, R.: A conservative finite element method for the Korteweg-de Vries equation. Math. Comput. 34(149), 23\u201343 (1980)","journal-title":"Math. Comput."},{"issue":"2","key":"455_CR51","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1016\/j.jcp.2003.11.009","volume":"196","author":"CJ Xu","year":"2004","unstructured":"Xu, C.J., Pasquetti, R.: Stabilized spectral element computations of high Reynolds number incompressible flows. J. Comput. Phys. 196(2), 680\u2013704 (2004)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"455_CR52","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1137\/11082258X","volume":"50","author":"Y Xu","year":"2012","unstructured":"Xu, Y., Shu, C.W.: Optimal error estimates of the semidiscrete local discontinuous Galerkin methods for high order wave equations. SIAM J. Numer. Anal. 50(1), 79\u2013104 (2012)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1\u20134","key":"455_CR53","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1023\/A:1015132126817","volume":"17","author":"J Yan","year":"2002","unstructured":"Yan, J., Shu, C.-W.: Local discontinuous Galerkin methods for partial differential equations with higher order derivatives. J. Sci. Comput. 17(1\u20134), 27\u201347 (2002)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"455_CR54","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1137\/S0036142901390378","volume":"40","author":"J Yan","year":"2002","unstructured":"Yan, J., Shu, C.-W.: A local discontinuous Galerkin method for KdV type equations. SIAM J. Numer. Anal. 40(2), 769\u2013791 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"455_CR55","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.jcp.2013.01.031","volume":"242","author":"N Yi","year":"2013","unstructured":"Yi, N., Huang, Y., Liu, H.: A direct discontinuous Galerkin method for the generalized Korteweg-de Vries equation: energy conservation and boundary effect. J. Comput. Phys. 242, 351\u2013366 (2013)","journal-title":"J. Comput. Phys."},{"issue":"6","key":"455_CR56","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1103\/PhysRevLett.15.240","volume":"15","author":"NJ Zabusky","year":"1965","unstructured":"Zabusky, N.J., Kruskal, M.D.: Interaction of solitons in a collisionless plasma and the recurence of initial states. Phys. Rev. Lett. 15(6), 240\u2013243 (1965)","journal-title":"Phys. Rev. Lett."},{"key":"455_CR57","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/S0045-7825(99)00142-5","volume":"188","author":"SI Zaki","year":"2000","unstructured":"Zaki, S.I.: A quintic B-spline finite elements scheme for the KdVB equation. J. Comput. Methods Appl. Mech. Eng. 188, 121\u2013134 (2000)","journal-title":"J. Comput. Methods Appl. Mech. Eng."},{"key":"455_CR58","doi-asserted-by":"crossref","first-page":"3613","DOI":"10.1088\/0305-4470\/33\/18\/308","volume":"33","author":"P Zhao","year":"2000","unstructured":"Zhao, P., Qin, M.: Multisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation. J. Phys. A Math. Gen. 33, 3613\u20133626 (2000)","journal-title":"J. Phys. A Math. Gen."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0455-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0455-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0455-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,28]],"date-time":"2022-07-28T22:15:55Z","timestamp":1659046555000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0455-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,26]]},"references-count":58,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["455"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0455-2","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2017,5,26]]}}}