{"id":"https://openalex.org/W2161202381","doi":"https://doi.org/10.1137/060657911","title":"Convergence of Godunov-Type Schemes for Scalar Conservation Laws under Large Time Steps","display_name":"Convergence of Godunov-Type Schemes for Scalar Conservation Laws under Large Time Steps","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2161202381","doi":"https://doi.org/10.1137/060657911","mag":"2161202381"},"language":"en","primary_location":{"id":"doi:10.1137/060657911","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060657911","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/A5065678545","display_name":"Jing\u2010Mei Qiu","orcid":"https://orcid.org/0000-0002-4226-6080"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jing-Mei Qiu","raw_affiliation_strings":["jqiu@dam.brown.edu and shu@dam.brown.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"jqiu@dam.brown.edu and shu@dam.brown.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047035333","display_name":"Chi\u2010Wang Shu","orcid":"https://orcid.org/0000-0001-7720-9564"},"institutions":[{"id":"https://openalex.org/I175594653","display_name":"John Brown University","ror":"https://ror.org/02ct41q97","country_code":"US","type":"education","lineage":["https://openalex.org/I175594653"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chi-Wang Shu","raw_affiliation_strings":["Brown University"],"affiliations":[{"raw_affiliation_string":"Brown University","institution_ids":["https://openalex.org/I175594653"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065678545"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.056,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.91745802,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"46","issue":"5","first_page":"2211","last_page":"2237"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9995999932289124,"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":0.9995999932289124,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9973999857902527,"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/conservation-law","display_name":"Conservation law","score":0.8472194671630859},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8273462057113647},{"id":"https://openalex.org/keywords/godunovs-scheme","display_name":"Godunov's scheme","score":0.7897744178771973},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5996078252792358},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5366458892822266},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5312995910644531},{"id":"https://openalex.org/keywords/bounded-variation","display_name":"Bounded variation","score":0.512385904788971},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5110710859298706},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.446156769990921},{"id":"https://openalex.org/keywords/total-variation-diminishing","display_name":"Total variation diminishing","score":0.4444934129714966},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36861056089401245},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34865662455558777},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.33268463611602783},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13015395402908325}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.8472194671630859},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8273462057113647},{"id":"https://openalex.org/C146705398","wikidata":"https://www.wikidata.org/wiki/Q4291826","display_name":"Godunov's scheme","level":3,"score":0.7897744178771973},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5996078252792358},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5366458892822266},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5312995910644531},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.512385904788971},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5110710859298706},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.446156769990921},{"id":"https://openalex.org/C152284280","wikidata":"https://www.wikidata.org/wiki/Q7828154","display_name":"Total variation diminishing","level":2,"score":0.4444934129714966},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36861056089401245},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34865662455558777},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.33268463611602783},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13015395402908325},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060657911","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060657911","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:ADA458955","is_oa":false,"landing_page_url":"http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA458955","pdf_url":null,"source":{"id":"https://openalex.org/S4406923043","display_name":"Defense Technical Information Center (DTIC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"DTIC","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.943.113","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.943.113","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dtic.mil/get-tr-doc/pdf?AD%3DADA458955%26Location%3DU2%26doc%3DGetTRDoc.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","score":0.5899999737739563,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1601100443","https://openalex.org/W1813101009","https://openalex.org/W1886421468","https://openalex.org/W1977534118","https://openalex.org/W1990340775","https://openalex.org/W1993281803","https://openalex.org/W1998830482","https://openalex.org/W2011669849","https://openalex.org/W2020600175","https://openalex.org/W2022818818","https://openalex.org/W2025982575","https://openalex.org/W2028550140","https://openalex.org/W2034342348","https://openalex.org/W2034976587","https://openalex.org/W2038547118","https://openalex.org/W2039150507","https://openalex.org/W2039241950","https://openalex.org/W2047497215","https://openalex.org/W2049778555","https://openalex.org/W2054662916","https://openalex.org/W2071942892","https://openalex.org/W2074264643","https://openalex.org/W2087149055","https://openalex.org/W2112548197","https://openalex.org/W4236438452","https://openalex.org/W4236518792"],"related_works":["https://openalex.org/W2091196763","https://openalex.org/W2097201125","https://openalex.org/W632617093","https://openalex.org/W2364357611","https://openalex.org/W3204799006","https://openalex.org/W3144960475","https://openalex.org/W2111445914","https://openalex.org/W2141851437","https://openalex.org/W2050140952","https://openalex.org/W2041609367"],"abstract_inverted_index":{"In":[0],"this":[1,70,98],"paper,":[2],"we":[3,48,100],"consider":[4],"convergence":[5,27,103],"of":[6,32,54,86,97],"classical":[7],"high-order":[8,63],"Godunov-type":[9,91],"schemes":[10],"towards":[11],"entropy":[12,39],"solutions":[13],"for":[14,25,108],"scalar":[15],"conservation":[16,80],"laws.":[17],"It":[18],"is":[19],"well":[20],"known":[21],"that":[22,43],"sufficient":[23,71],"conditions":[24],"such":[26,59,87],"include":[28],"total":[29,51,64,118],"variation":[30,52,65,119],"boundedness":[31,53],"the":[33,55,84,95],"reconstruction":[34,56,121],"and":[35,73,104,126],"cell":[36,124,130],"or":[37],"wavewise":[38],"inequalities.":[40],"We":[41,61],"prove":[42,102],"under":[44],"large":[45,88,110],"time":[46,89,111],"steps,":[47],"only":[49],"need":[50],"to":[57,68,82],"guarantee":[58],"convergence.":[60],"discuss":[62],"bounded":[66],"reconstructions":[67],"fulfill":[69],"condition":[72],"provide":[74],"numerical":[75,106],"examples":[76,107],"on":[77],"one-dimensional":[78],"convex":[79],"laws":[81],"assess":[83],"performance":[85],"step":[90,112],"methods.":[92],"To":[93],"demonstrate":[94],"generality":[96],"approach,":[99],"also":[101],"give":[105],"a":[109],"Godunov-like":[113],"scheme":[114],"involving":[115],"Sanders'":[116],"third-order":[117],"diminishing":[120],"using":[122],"both":[123],"averages":[125],"point":[127],"values":[128],"at":[129],"boundaries.":[131]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}