{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T02:49:38Z","timestamp":1768704578689,"version":"3.49.0"},"reference-count":45,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2015,5,1]],"date-time":"2015-05-01T00:00:00Z","timestamp":1430438400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational Physics"],"published-print":{"date-parts":[[2015,5]]},"DOI":"10.1016\/j.jcp.2015.02.041","type":"journal-article","created":{"date-parts":[[2015,3,2]],"date-time":"2015-03-02T17:00:46Z","timestamp":1425315646000},"page":"181-195","update-policy":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":36,"special_numbering":"C","title":["Positivity preserving high-order local discontinuous Galerkin method for parabolic equations with blow-up solutions"],"prefix":"10.1016","volume":"289","author":[{"given":"Li","family":"Guo","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0000-0002-0621-1226","authenticated-orcid":false,"given":"Yang","family":"Yang","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.jcp.2015.02.041_br0010","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/S0168-9274(97)00105-0","article-title":"On the blow-up time convergence of semidiscretizations of reaction\u2013diffusion equations","volume":"26","author":"Abia","year":"1998","journal-title":"Appl. Numer. Math."},{"key":"10.1016\/j.jcp.2015.02.041_br0020","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s00607-002-1449-x","article-title":"An adaptive time step procedure for a parabolic problem with blow-up","volume":"68","author":"Acosta","year":"2002","journal-title":"Computing"},{"key":"10.1016\/j.jcp.2015.02.041_br0030","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1006\/jcph.1996.5572","article-title":"A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier\u2013Stokes equations","volume":"131","author":"Bassi","year":"1997","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2015.02.041_br0040","series-title":"Mathematical Problems from Combustion Theory","author":"Bebernes","year":"1989"},{"key":"10.1016\/j.jcp.2015.02.041_br0050","first-page":"187","article-title":"On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order","volume":"21","author":"Boni","year":"1999","journal-title":"Asymptot. Anal."},{"key":"10.1016\/j.jcp.2015.02.041_br0060","first-page":"73","article-title":"Blow-up of ut=uxx+g(u) revisited","volume":"1","author":"Brezis","year":"1996","journal-title":"Adv. Differ. Equ."},{"key":"10.1016\/j.jcp.2015.02.041_br0070","first-page":"203","article-title":"Numerical analysis of semilinear parabolic problems with blow-up solutions","volume":"88","author":"Bandle","year":"1994","journal-title":"Rev. R. Acad. Cienc. Exactas F\u00eds. Nat."},{"key":"10.1016\/j.jcp.2015.02.041_br0080","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0377-0427(98)00100-9","article-title":"Blowup in diffusion equations: a survey","volume":"97","author":"Bandle","year":"1998","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.jcp.2015.02.041_br0090","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1142\/S0218202504003751","article-title":"Fully discrete adaptive methods for a blow-up problem","volume":"14","author":"Br\u00e4ndle","year":"2004","journal-title":"Math. Models Methods Appl. Sci."},{"key":"10.1016\/j.jcp.2015.02.041_br0100","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s00211-005-0638-x","article-title":"An adaptive numerical method to handle blow-up in a parabolic system","volume":"102","author":"Br\u00e4ndle","year":"2005","journal-title":"Numer. Math."},{"key":"10.1016\/j.jcp.2015.02.041_br0110","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1137\/S1064827594272025","article-title":"Moving mesh methods for problems with blow-up","volume":"17","author":"Budd","year":"1996","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.jcp.2015.02.041_br0120","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1090\/S0025-5718-07-02045-5","article-title":"A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives","volume":"77","author":"Cheng","year":"2008","journal-title":"Math. Comput."},{"key":"10.1016\/j.jcp.2015.02.041_br0130","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.apnum.2012.11.001","article-title":"On the finite difference approximation for blow-up solutions of the porous medium equation with a source","volume":"65","author":"Cho","year":"2013","journal-title":"Appl. Numer. Math."},{"key":"10.1016\/j.jcp.2015.02.041_br0140","first-page":"545","article-title":"The Runge\u2013Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case","volume":"54","author":"Cockburn","year":"1990","journal-title":"Math. Comput."},{"key":"10.1016\/j.jcp.2015.02.041_br0150","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/0021-9991(89)90183-6","article-title":"TVB Runge\u2013Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems","volume":"84","author":"Cockburn","year":"1989","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2015.02.041_br0160","first-page":"411","article-title":"TVB Runge\u2013Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework","volume":"52","author":"Cockburn","year":"1989","journal-title":"Math. Comput."},{"key":"10.1016\/j.jcp.2015.02.041_br0170","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1006\/jcph.1998.5892","article-title":"The Runge\u2013Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems","volume":"141","author":"Cockburn","year":"1998","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2015.02.041_br0180","doi-asserted-by":"crossref","first-page":"2440","DOI":"10.1137\/S0036142997316712","article-title":"The local discontinuous Galerkin method for time dependent convection\u2013diffusion systems","volume":"35","author":"Cockburn","year":"1998","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.jcp.2015.02.041_br0190","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s10915-007-9130-3","article-title":"An analysis of the minimal dissipation local discontinuous Galerkin method for convection\u2013diffusion problems","volume":"32","author":"Cockburn","year":"2007","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.jcp.2015.02.041_br0200","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1142\/S021820250200174X","article-title":"Numerical blow-up for a nonlinear problem with a nonlinear boundary condition","volume":"12","author":"Ferreira","year":"2002","journal-title":"Math. Models Methods Appl. Sci."},{"key":"10.1016\/j.jcp.2015.02.041_br0210","doi-asserted-by":"crossref","first-page":"399","DOI":"10.3934\/dcds.2002.8.399","article-title":"The problem of blow-up in nonlinear parabolic equation","volume":"8","author":"Galaktionov","year":"2002","journal-title":"Discrete Contin. Dyn. Syst."},{"key":"10.1016\/j.jcp.2015.02.041_br0220","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s00607-005-0136-0","article-title":"Totally discrete explicit and semi-implicit Euler methods for a blow-up problem in several space dimensions","volume":"76","author":"Groisman","year":"2006","journal-title":"Computing"},{"key":"10.1016\/j.jcp.2015.02.041_br0230","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1137\/S003614450036757X","article-title":"Strong stability-preserving high-order time discretization methods","volume":"43","author":"Gottlieb","year":"2001","journal-title":"SIAM Rev."},{"key":"10.1016\/j.jcp.2015.02.041_br0240","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0025-5718-1986-0815828-4","article-title":"An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation","volume":"46","author":"Johnson","year":"1986","journal-title":"Math. Comput."},{"key":"10.1016\/j.jcp.2015.02.041_br0250","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1007\/s10114-009-7048-4","article-title":"Global existence and uniqueness of weak solution to nonlinear viscoelastic full Marguerre\u2013von K\u00e1rm\u00e1n shallow equations","volume":"25","author":"Li","year":"2009","journal-title":"Acta Math. Sin. Engl. Ser."},{"key":"10.1016\/j.jcp.2015.02.041_br0260","doi-asserted-by":"crossref","first-page":"695","DOI":"10.2977\/prims\/1195169267","article-title":"On blow-up of solutions for quasilinear degenerate parabolic equations","volume":"27","author":"Mai","year":"1991","journal-title":"Publ. Res. Inst. Math. Sci."},{"key":"10.1016\/j.jcp.2015.02.041_br0270","first-page":"173","article-title":"Blow-up for semidiscretization of a localized semilinear heat equation","volume":"2","author":"Nabongo","year":"2009","journal-title":"J. Appl. Anal."},{"key":"10.1016\/j.jcp.2015.02.041_br0280","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1007\/s10114-011-8464-9","article-title":"Numerical blow-up for a nonlinear heat equation","volume":"27","author":"N'Gohisse","year":"2011","journal-title":"Acta Math. Sin. Engl. Ser."},{"key":"10.1016\/j.jcp.2015.02.041_br0290","article-title":"Superlinear Parabolic Problems","author":"Quittner","year":"2007"},{"key":"10.1016\/j.jcp.2015.02.041_br0300","series-title":"Triangular mesh methods for the Neutron transport equation","author":"Reed","year":"1973"},{"key":"10.1016\/j.jcp.2015.02.041_br0310","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1137\/0731009","article-title":"Semidiscretization in time of nonlinear parabolic equations with blow-up of the solution","volume":"31","author":"Le Roux","year":"1994","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.jcp.2015.02.041_br0320","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1137\/0909073","article-title":"Total-variation-diminishing time discretizations","volume":"9","author":"Shu","year":"1988","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"10.1016\/j.jcp.2015.02.041_br0330","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/0021-9991(88)90177-5","article-title":"Efficient implementation of essentially non-oscillatory shock-capturing schemes","volume":"77","author":"Shu","year":"1988","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2015.02.041_br0340","doi-asserted-by":"crossref","first-page":"375","DOI":"10.2977\/prims\/1195169661","article-title":"On blow-up sets and asymptotic behavior of interface of one dimensional quasilinear degenerate parabolic equation","volume":"27","author":"Suzuki","year":"1991","journal-title":"Publ. Res. Inst. Math. Sci."},{"key":"10.1016\/j.jcp.2015.02.041_br0350","doi-asserted-by":"crossref","first-page":"613","DOI":"10.2977\/prims\/1195142812","article-title":"On the approximation of blow-up time for solutions of nonlinear parabolic equations","volume":"36","author":"Ushijima","year":"2000","journal-title":"Publ. Res. Inst. Math. Sci."},{"key":"10.1016\/j.jcp.2015.02.041_br0360","unstructured":"T. Xiong, J.-M. Qiu, Z. Xu, A maximum principle preserving limiter for discontinuous Galerkin method with applications to convection\u2013diffusion equations, submitted for publication."},{"key":"10.1016\/j.jcp.2015.02.041_br0370","doi-asserted-by":"crossref","first-page":"2213","DOI":"10.1090\/S0025-5718-2013-02788-3","article-title":"Parametrized maximum principle preserving flux limiters for high order schemes solving hyperbolic conservation laws: one-dimensional scalar problem","volume":"83","author":"Xu","year":"2014","journal-title":"Math. Comput."},{"key":"10.1016\/j.jcp.2015.02.041_br0380","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1007\/s00211-013-0526-8","article-title":"Discontinuous Galerkin methods for hyperbolic equations involving \u03b4-singularities: negative-order norm error estimates and applications","volume":"124","author":"Yang","year":"2013","journal-title":"Numer. Math."},{"key":"10.1016\/j.jcp.2015.02.041_br0390","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.jcp.2013.06.015","article-title":"Discontinuous Galerkin method for Krause's consensus models and pressureless Euler equations","volume":"252","author":"Yang","year":"2013","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2015.02.041_br0400","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1016\/j.jcp.2014.08.044","article-title":"A positivity-preserving semi-implicit discontinuous Galerkin scheme for solving extended magnetohydrodynamics equations","volume":"278","author":"Zhao","year":"2014","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2015.02.041_br0410","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/s10114-010-8127-2","article-title":"Parabolic equation with VMO coefficients in generalized Morrey","volume":"26","author":"Zhang","year":"2010","journal-title":"Acta Math. Sin. Engl. Ser."},{"key":"10.1016\/j.jcp.2015.02.041_br0420","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10915-008-9223-7","article-title":"Numerical simulation for porous medium equation by local discontinuous Galerkin finite element method","volume":"38","author":"Zhang","year":"2009","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.jcp.2015.02.041_br0430","doi-asserted-by":"crossref","first-page":"3091","DOI":"10.1016\/j.jcp.2009.12.030","article-title":"On maximum-principle-satisfying high order schemes for scalar conservation laws","volume":"229","author":"Zhang","year":"2010","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2015.02.041_br0440","doi-asserted-by":"crossref","first-page":"8918","DOI":"10.1016\/j.jcp.2010.08.016","article-title":"On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes","volume":"229","author":"Zhang","year":"2010","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2015.02.041_br0450","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/j.jcp.2012.09.032","article-title":"Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection\u2013diffusion equations on triangular meshes","volume":"234","author":"Zhang","year":"2013","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Computational Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/api.elsevier.com\/content\/article\/PII:S0021999115001114?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/api.elsevier.com\/content\/article\/PII:S0021999115001114?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,8,30]],"date-time":"2020-08-30T12:03:16Z","timestamp":1598788996000},"score":1,"resource":{"primary":{"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/linkinghub.elsevier.com\/retrieve\/pii\/S0021999115001114"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5]]},"references-count":45,"alternative-id":["S0021999115001114"],"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/doi.org\/10.1016\/j.jcp.2015.02.041","relation":{},"ISSN":["0021-9991"],"issn-type":[{"value":"0021-9991","type":"print"}],"subject":[],"published":{"date-parts":[[2015,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Positivity preserving high-order local discontinuous Galerkin method for parabolic equations with blow-up solutions","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational Physics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/doi.org\/10.1016\/j.jcp.2015.02.041","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2015 Elsevier Inc. All rights reserved.","name":"copyright","label":"Copyright"}]}}