{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T12:35:21Z","timestamp":1768566921982,"version":"3.49.0"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,2,8]],"date-time":"2016-02-08T00:00:00Z","timestamp":1454889600000},"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":["J Sci Comput"],"published-print":{"date-parts":[[2016,9]]},"DOI":"10.1007\/s10915-016-0170-4","type":"journal-article","created":{"date-parts":[[2016,2,8]],"date-time":"2016-02-08T03:58:48Z","timestamp":1454903928000},"page":"1029-1054","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Efficient High Order Semi-implicit Time Discretization and Local Discontinuous Galerkin Methods for Highly Nonlinear PDEs"],"prefix":"10.1007","volume":"68","author":[{"given":"Ruihan","family":"Guo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francis","family":"Filbet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,2,8]]},"reference":[{"key":"170_CR1","doi-asserted-by":"crossref","unstructured":"Bassi, F., Rebay, S.: A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier\u2013Stokes equations. J. Comput. Phys. 131, 267\u2013279 (1997)","DOI":"10.1006\/jcph.1996.5572"},{"key":"170_CR2","doi-asserted-by":"publisher","unstructured":"Boscarino, S., Filbet, F., Russo, G.: High order semi-implicit schemes for time dependent partial differential equations. J. Sci. Comput. 66, 1\u201327 (2016). doi: 10.1007\/s10915-016-0168-y","DOI":"10.1007\/s10915-016-0168-y"},{"key":"170_CR3","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 conservation laws II: general framework. Math. Comput. 52, 411\u2013435 (1989)","journal-title":"Math. Comput."},{"key":"170_CR4","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":"170_CR5","first-page":"545","volume":"54","author":"B Cockburn","year":"1990","unstructured":"Cockburn, B., Hou, S., Shu, C.-W.: The Runge\u2013Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case. Math. Comput. 54, 545\u2013581 (1990)","journal-title":"Math. Comput."},{"key":"170_CR6","doi-asserted-by":"crossref","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":"170_CR7","doi-asserted-by":"crossref","first-page":"2440","DOI":"10.1137\/S0036142997316712","volume":"35","author":"B Cockburn","year":"1998","unstructured":"Cockburn, B., Shu, C.-W.: The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35, 2440\u20132463 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"170_CR8","doi-asserted-by":"crossref","first-page":"21","DOI":"10.4171\/IFB\/134","volume":"8","author":"K Deckelnick","year":"2006","unstructured":"Deckelnick, K., Dziuk, G.: Error analysis of a finite element method for the Willmore flow of graphs. Interfaces Free Bound. 8, 21\u201346 (2006)","journal-title":"Interfaces Free Bound."},{"key":"170_CR9","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1023\/A:1022338906936","volume":"40","author":"A Dutt","year":"2000","unstructured":"Dutt, A., Greengard, L., Rokhlin, V.: Spectral deferred correction methods for ordinary differential equations. BIT 40, 241\u2013266 (2000)","journal-title":"BIT"},{"key":"170_CR10","first-page":"1685","volume-title":"Computational and Mathematical Models of Microstructural Evolution","author":"DJ Eyre","year":"1998","unstructured":"Eyre, D.J.: Unconditionally gradient stable time marching the Cahn\u2013Hilliard equation. In: Bullard, J.W., Kalia, R., Stoneham, M., Chen, L.Q. (eds.) Computational and Mathematical Models of Microstructural Evolution, vol. 53, pp. 1685\u20131712. Materials Research Society, Warrendale (1998)"},{"issue":"2","key":"170_CR11","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1007\/s10915-010-9394-x","volume":"46","author":"F Filbet","year":"2011","unstructured":"Filbet, F., Jin, S.: An asymptotic preserving scheme for the ES-BGK model of the Boltzmann equation. J. Sci. Comput. 46(2), 204\u2013224 (2011)","journal-title":"J. Sci. Comput."},{"issue":"20","key":"170_CR12","doi-asserted-by":"crossref","first-page":"7625","DOI":"10.1016\/j.jcp.2010.06.017","volume":"229","author":"F Filbet","year":"2010","unstructured":"Filbet, F., Jin, S.: A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources. J. Comput. Phys. 229(20), 7625\u20137648 (2010)","journal-title":"J. Comput. Phys."},{"key":"170_CR13","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1007\/s10915-013-9738-4","volume":"58","author":"R Guo","year":"2014","unstructured":"Guo, R., Xu, Y.: Efficient solvers of discontinuous Galerkin discretization for the Cahn\u2013Hilliard equations. J. Sci. Comput. 58, 380\u2013408 (2014)","journal-title":"J. Sci. Comput."},{"key":"170_CR14","first-page":"471","volume":"1","author":"ML Minion","year":"2003","unstructured":"Minion, M.L.: Semi-implicit spectral deferred correction methods for ordinary differential equations. Math. Sci. 1, 471\u2013500 (2003)","journal-title":"Math. Sci."},{"key":"170_CR15","unstructured":"Pareschi, L., Russo, G.: Implicit-Explicit Runge\u2013Kutta Schemes for Stiff Systems of Differential Equations. Recent trends in numerical analysis, pp. 269\u2013288, Adv. Theory Comput. Math. 3, Nova Sci. Publ. Huntington (2001)"},{"key":"170_CR16","volume-title":"Triangular Mesh Method for the Neutron Transport Equation, Technical Report LA-UR-73-479","author":"WH Reed","year":"1973","unstructured":"Reed, W.H., Hill, T.R.: Triangular Mesh Method for the Neutron Transport Equation, Technical Report LA-UR-73-479. Los Alamos Scientific Laboratory, Los Alamos (1973)"},{"key":"170_CR17","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1023\/A:1025324613450","volume":"19","author":"P Smereka","year":"2003","unstructured":"Smereka, P.: Semi-implicit level set methods for curvature and surface diffusion motion. J. Sci. Comput. 19, 439\u2013456 (2003)","journal-title":"J. Sci. Comput."},{"key":"170_CR18","volume-title":"Multigrid","author":"U Trottenberg","year":"2005","unstructured":"Trottenberg, U., Oosterlee, C., Sch\u00fcller, A.: Multigrid. Academic Press, New York (2005)"},{"key":"170_CR19","first-page":"677","volume":"227","author":"Y Xia","year":"2007","unstructured":"Xia, Y., Xu, Y., Shu, C.-W.: Local discontinuous Galerkin methods for the Cahn\u2013Hilliard type equations. J. Comput. Phys. 227, 677\u2013693 (2007)","journal-title":"J. Comput. Phys."},{"key":"170_CR20","doi-asserted-by":"crossref","first-page":"677","DOI":"10.3934\/dcdsb.2007.8.677","volume":"8","author":"Y Xia","year":"2007","unstructured":"Xia, Y., Xu, Y., Shu, C.-W.: Efficient time discretization for local discontinuous Galerkin methods. Discrete Contin. Dyn. Syst. Ser. B 8, 677\u2013693 (2007)","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"key":"170_CR21","first-page":"821","volume":"5","author":"Y Xia","year":"2009","unstructured":"Xia, Y., Xu, Y., Shu, C.-W.: Application of the local discontinuous Galerkin method for the Allen\u2013Cahn\/Cahn\u2013Hilliard system. Commun. Comput. Phys. 5, 821\u2013835 (2009)","journal-title":"Commun. Comput. Phys."},{"key":"170_CR22","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/j.jcp.2014.09.025","volume":"280","author":"Y Xia","year":"2015","unstructured":"Xia, Y.: A fully discrete stable discontinuous Galerkin method for the thin film epitaxy problem without slope selection. J. Comput. Phys. 280, 248\u2013260 (2015)","journal-title":"J. Comput. Phys."},{"key":"170_CR23","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s10915-008-9262-0","volume":"40","author":"Y Xu","year":"2009","unstructured":"Xu, Y., Shu, C.-W.: Local discontinuous Galerkin method for surface diffusion and Willmore flow of graphs. J. Sci. Comput. 40, 375\u2013390 (2009)","journal-title":"J. Sci. Comput."},{"key":"170_CR24","first-page":"1","volume":"7","author":"Y Xu","year":"2010","unstructured":"Xu, Y., Shu, C.-W.: Local discontinuous Galerkin methods for high-order time-dependent partial differential equations. Commun. Comput. Phys. 7, 1\u201346 (2010)","journal-title":"Commun. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0170-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-016-0170-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0170-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T08:45:55Z","timestamp":1559465155000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-016-0170-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,8]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,9]]}},"alternative-id":["170"],"URL":"https:\/\/doi.org\/10.1007\/s10915-016-0170-4","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,8]]}}}