{"id":"https://openalex.org/W2038327721","doi":"https://doi.org/10.1137/s0036142999363668","title":"Convergence of a Difference Scheme for Conservation Laws with a Discontinuous Flux","display_name":"Convergence of a Difference Scheme for Conservation Laws with a Discontinuous Flux","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2038327721","doi":"https://doi.org/10.1137/s0036142999363668","mag":"2038327721"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142999363668","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999363668","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/A5079737050","display_name":"John D. Towers","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"John D. Towers","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079737050"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.3073,"has_fulltext":false,"cited_by_count":171,"citation_normalized_percentile":{"value":0.97925349,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"38","issue":"2","first_page":"681","last_page":"698"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9983999729156494,"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":0.9983999729156494,"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":0.996999979019165,"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":0.9954000115394592,"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/mathematics","display_name":"Mathematics","score":0.8818471431732178},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.858298659324646},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6553913354873657},{"id":"https://openalex.org/keywords/riemann-problem","display_name":"Riemann problem","score":0.6075952053070068},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.541570782661438},{"id":"https://openalex.org/keywords/godunovs-scheme","display_name":"Godunov's scheme","score":0.5385547280311584},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5269563794136047},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48576024174690247},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.480509877204895},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.4801989793777466},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.44094011187553406},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.23246118426322937},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1317410171031952},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.062315672636032104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8818471431732178},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.858298659324646},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6553913354873657},{"id":"https://openalex.org/C40709475","wikidata":"https://www.wikidata.org/wiki/Q2152221","display_name":"Riemann problem","level":3,"score":0.6075952053070068},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.541570782661438},{"id":"https://openalex.org/C146705398","wikidata":"https://www.wikidata.org/wiki/Q4291826","display_name":"Godunov's scheme","level":3,"score":0.5385547280311584},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5269563794136047},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48576024174690247},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.480509877204895},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.4801989793777466},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.44094011187553406},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.23246118426322937},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1317410171031952},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.062315672636032104},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036142999363668","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999363668","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:10.1.1.40.8209","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.8209","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ntnu.no/conservation/1999/024.ps","raw_type":"text"},{"id":"pmh:oai:bibcyt.ucla.edu.ve:T070300010721/17","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300010721/17&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":[{"score":0.6600000262260437,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1601100443","https://openalex.org/W1967167841","https://openalex.org/W1967575591","https://openalex.org/W1969830344","https://openalex.org/W1972578258","https://openalex.org/W1986788497","https://openalex.org/W1988634891","https://openalex.org/W1992812527","https://openalex.org/W1998483100","https://openalex.org/W2013770958","https://openalex.org/W2020168202","https://openalex.org/W2023343093","https://openalex.org/W2025473292","https://openalex.org/W2026388260","https://openalex.org/W2031171101","https://openalex.org/W2034939914","https://openalex.org/W2034976587","https://openalex.org/W2038831503","https://openalex.org/W2038991247","https://openalex.org/W2042314743","https://openalex.org/W2043358921","https://openalex.org/W2045679525","https://openalex.org/W2049710887","https://openalex.org/W2050738224","https://openalex.org/W2056826596","https://openalex.org/W2058221859","https://openalex.org/W2066501150","https://openalex.org/W2080202186","https://openalex.org/W2778033595","https://openalex.org/W4232013057","https://openalex.org/W4292081050","https://openalex.org/W4297084762"],"related_works":["https://openalex.org/W632617093","https://openalex.org/W4295135832","https://openalex.org/W2364357611","https://openalex.org/W2520772736","https://openalex.org/W4251559080","https://openalex.org/W4240076417","https://openalex.org/W2020017862","https://openalex.org/W2043057066","https://openalex.org/W4231519251","https://openalex.org/W2036952581"],"abstract_inverted_index":{".":[0],"Convergence":[1],"is":[2,25,67,85,127],"established":[3,39,68],"for":[4,17,41,69,94,132,140],"a":[5,22,29,61,80,101,128],"scalar":[6,18,56],"nite":[7,129],"dierence":[8,109,130],"scheme,":[9],"based":[10],"on":[11],"the":[12,44,70,137],"Godunov":[13],"or":[14],"Engquist-Osher":[15],"ux,":[16],"conservation":[19,107],"laws":[20],"having":[21],"ux":[23],"that":[24,87],"spatially":[26],"dependent":[27],"through":[28],"possibly":[30],"discontinuous":[31,111],"coecient.":[32],"Other":[33],"works":[34],"in":[35],"this":[36,125],"direction":[37],"have":[38],"convergence":[40],"methods":[42],"employing":[43],"solution":[45],"of":[46,60,63,124,136],"2x2":[47],"Riemann":[48,57],"problems.":[49],"The":[50,122],"algorithm":[51,131],"discussed":[52],"here":[53],"uses":[54],"only":[55],"solvers.":[58],"Satisfaction":[59],"set":[62],"Kruzkov-type":[64],"entropy":[65,76],"inequalities":[66],"limit":[71],"solution,":[72],"from":[73],"which":[74],"geometric":[75],"conditions":[77,89],"follow.":[78],"Assuming":[79],"piecewise":[81,95],"constant":[82],"coecient,":[83],"it":[84],"shown":[86],"these":[88],"imply":[90],"L":[91],"1":[92,97],"-contractiveness":[93],"C":[96],"solutions,":[98],"thus":[99],"extending":[100],"well":[102],"known":[103],"theorem.":[104],"Key":[105],"words.":[106],"laws,":[108],"approximations,":[110],"coecients":[112],"AMS":[113],"subject":[114,123],"classications.":[115],"35L65,":[116],"65M06,":[117],"65M12,":[118],"35R05":[119],"1.":[120],"Introduction.":[121],"paper":[126],"computing":[133],"approximate":[134],"solutions":[135],"Cauchy":[138],"problem":[139],"scala...":[141]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}