{"id":"https://openalex.org/W1981127395","doi":"https://doi.org/10.1137/s0036142901388627","title":"Conservative Front Tracking with Improved Accuracy","display_name":"Conservative Front Tracking with Improved Accuracy","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1981127395","doi":"https://doi.org/10.1137/s0036142901388627","mag":"1981127395"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142901388627","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901388627","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038334215","display_name":"James Glimm","orcid":null},"institutions":[{"id":"https://openalex.org/I200870766","display_name":"Brookhaven National Laboratory","ror":"https://ror.org/02ex6cf31","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I200870766","https://openalex.org/I39565521","https://openalex.org/I4210142672"]},{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Glimm","raw_affiliation_strings":["Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY 11794-3600","Center for Data Intensive Computing, Brookhaven National Laboratory, Upton, NY 11793-5000"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY 11794-3600","institution_ids":["https://openalex.org/I59553526"]},{"raw_affiliation_string":"Center for Data Intensive Computing, Brookhaven National Laboratory, Upton, NY 11793-5000","institution_ids":["https://openalex.org/I200870766"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100353697","display_name":"Xiaolin Li","orcid":"https://orcid.org/0000-0001-5899-5651"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaolin Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100384082","display_name":"Yingjie Liu","orcid":"https://orcid.org/0000-0002-3551-6635"},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yingjie Liu","raw_affiliation_strings":["Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY 11794-3600"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY 11794-3600","institution_ids":["https://openalex.org/I59553526"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100600729","display_name":"Zhiliang Xu","orcid":"https://orcid.org/0000-0002-4682-9442"},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhiliang Xu","raw_affiliation_strings":["Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY 11794-3600"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY 11794-3600","institution_ids":["https://openalex.org/I59553526"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000038985","display_name":"Ning Zhao","orcid":"https://orcid.org/0000-0002-2802-2581"},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]},{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Ning Zhao","raw_affiliation_strings":["Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY 11794-3600","Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY 11794-3600","institution_ids":["https://openalex.org/I59553526"]},{"raw_affiliation_string":"Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.4267,"has_fulltext":false,"cited_by_count":127,"citation_normalized_percentile":{"value":0.96700774,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"41","issue":"5","first_page":"1926","last_page":"1947"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.863605260848999},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.7494852542877197},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.711136519908905},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.6002384424209595},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.5982844233512878},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5890911221504211},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.570968508720398},{"id":"https://openalex.org/keywords/front","display_name":"Front (military)","score":0.5683795213699341},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5238247513771057},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4870584309101105},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.4445212185382843},{"id":"https://openalex.org/keywords/order-of-accuracy","display_name":"Order of accuracy","score":0.4311453700065613},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3976103663444519},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.36564669013023376},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35436826944351196},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17073377966880798},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08473813533782959},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.07517588138580322},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.06571966409683228}],"concepts":[{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.863605260848999},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.7494852542877197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.711136519908905},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.6002384424209595},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.5982844233512878},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5890911221504211},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.570968508720398},{"id":"https://openalex.org/C2777551076","wikidata":"https://www.wikidata.org/wiki/Q842332","display_name":"Front (military)","level":2,"score":0.5683795213699341},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5238247513771057},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4870584309101105},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4445212185382843},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.4311453700065613},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3976103663444519},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.36564669013023376},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35436826944351196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17073377966880798},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08473813533782959},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.07517588138580322},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.06571966409683228},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036142901388627","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901388627","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.128.6391","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.128.6391","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.gatech.edu/~yingjie/publications/GLLXZ.pdf","raw_type":"text"},{"id":"pmh:oai:bibcyt.ucla.edu.ve:T070300013566/13","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300013566/13&Nombrebd=Bciucla","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.7200000286102295}],"awards":[{"id":"https://openalex.org/G4184270406","display_name":"MUILTISCALE STOCHASTIC        SIMULATION NAD MODELING","funder_award_id":"FG02-90ER25084","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7186324567","display_name":null,"funder_award_id":"DE-FG02-","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G734485876","display_name":"Conservation Laws for Multiphase Flow","funder_award_id":"0102480","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8684078510","display_name":null,"funder_award_id":"DE-FG02","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"},{"id":"https://openalex.org/F4320338304","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W98167876","https://openalex.org/W983099591","https://openalex.org/W1973558216","https://openalex.org/W1976684253","https://openalex.org/W1988619471","https://openalex.org/W1998602489","https://openalex.org/W1999342804","https://openalex.org/W2000114813","https://openalex.org/W2023016983","https://openalex.org/W2033130870","https://openalex.org/W2038991247","https://openalex.org/W2059257656","https://openalex.org/W2077229134","https://openalex.org/W2088575693","https://openalex.org/W2118078932","https://openalex.org/W2229412420","https://openalex.org/W4212916239","https://openalex.org/W4233857083","https://openalex.org/W4292081050"],"related_works":["https://openalex.org/W2323190011","https://openalex.org/W3039499377","https://openalex.org/W162062087","https://openalex.org/W2085032340","https://openalex.org/W2026226327","https://openalex.org/W1989965977","https://openalex.org/W2056095867","https://openalex.org/W2232767080","https://openalex.org/W1756153455","https://openalex.org/W2373997809"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,51],"fully":[3],"conservative":[4],"front":[5],"tracking":[6],"algorithm":[7,15,37],"for":[8],"systems":[9],"of":[10],"nonlinear":[11],"conservation":[12],"laws.":[13],"The":[14],"improves":[16],"by":[17],"one":[18],"order":[19],"in":[20,32],"its":[21],"convergence":[22],"rate":[23],"over":[24,44],"most":[25],"finite":[26],"difference":[27],"schemes.":[28],"Near":[29],"tracked":[30],"discontinuities":[31],"the":[33,35],"solution,":[34],"proposed":[36],"has":[38],"${\\mathcal":[39,45],"O}(\\Delta":[40],"x)$":[41],"errors,":[42],"improving":[43],"O}(1)$":[46],"errors":[47],"commonly":[48],"found":[49],"near":[50],"discontinuity.":[52],"Numerical":[53],"experiments":[54],"which":[55],"confirm":[56],"these":[57],"assertions":[58],"are":[59],"presented.":[60]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":6}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
