{"id":"https://openalex.org/W2125123420","doi":"https://doi.org/10.1137/s0036142999350383","title":"Two A Posteriori Error Estimates for One-Dimensional Scalar Conservation Laws","display_name":"Two A Posteriori Error Estimates for One-Dimensional Scalar Conservation Laws","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2125123420","doi":"https://doi.org/10.1137/s0036142999350383","mag":"2125123420"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142999350383","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999350383","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/A5057486912","display_name":"Laurent Gosse","orcid":"https://orcid.org/0000-0001-7482-254X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Laurent Gosse","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5105693474","display_name":"Charalambos Makridakis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Charalambos Makridakis","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057486912"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2153,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.87524616,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"38","issue":"3","first_page":"964","last_page":"988"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9991000294685364,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.9107142686843872},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8355725407600403},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6084822416305542},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5948988199234009},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.5851557850837708},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5841444730758667},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5687952637672424},{"id":"https://openalex.org/keywords/numerical-approximation","display_name":"Numerical approximation","score":0.42523157596588135},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4239358901977539},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.42015761137008667},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39569640159606934},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3229089081287384},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29634276032447815},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11827662587165833}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.9107142686843872},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8355725407600403},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6084822416305542},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5948988199234009},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.5851557850837708},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5841444730758667},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5687952637672424},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.42523157596588135},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4239358901977539},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.42015761137008667},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39569640159606934},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3229089081287384},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29634276032447815},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11827662587165833},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036142999350383","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999350383","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:10.1.1.310.8724","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.310.8724","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cscamm.umd.edu/people/faculty/tadmor/convergence_rate/Gosse_Makridakis_conservation_laws_SINUM00.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.50.302","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.302","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://palamida.math.uch.gr/laurent/ap_new.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.6700000166893005}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W91609649","https://openalex.org/W1537551582","https://openalex.org/W1580248330","https://openalex.org/W1601100443","https://openalex.org/W1967167841","https://openalex.org/W1967575591","https://openalex.org/W1971747754","https://openalex.org/W1975087281","https://openalex.org/W1977534118","https://openalex.org/W1988634891","https://openalex.org/W1989067183","https://openalex.org/W1990330990","https://openalex.org/W1992812527","https://openalex.org/W2003836934","https://openalex.org/W2008076987","https://openalex.org/W2009395216","https://openalex.org/W2010367041","https://openalex.org/W2011417962","https://openalex.org/W2013299358","https://openalex.org/W2020168202","https://openalex.org/W2023421695","https://openalex.org/W2025483160","https://openalex.org/W2025982575","https://openalex.org/W2042118059","https://openalex.org/W2043358921","https://openalex.org/W2047554497","https://openalex.org/W2048914028","https://openalex.org/W2050738224","https://openalex.org/W2066501150","https://openalex.org/W2066538206","https://openalex.org/W2067187920","https://openalex.org/W2080697504","https://openalex.org/W2086654907","https://openalex.org/W2091704977","https://openalex.org/W2100726453","https://openalex.org/W2112548197","https://openalex.org/W2146898032","https://openalex.org/W2168746862","https://openalex.org/W2464270290","https://openalex.org/W3216299223","https://openalex.org/W4233961755","https://openalex.org/W4237579110","https://openalex.org/W4243839716","https://openalex.org/W4247342202","https://openalex.org/W4255851310"],"related_works":["https://openalex.org/W2101741420","https://openalex.org/W1625146931","https://openalex.org/W2091193375","https://openalex.org/W1994495964","https://openalex.org/W1997932535","https://openalex.org/W2010049312","https://openalex.org/W2963771406","https://openalex.org/W2169403347","https://openalex.org/W2152819099","https://openalex.org/W2023399328"],"abstract_inverted_index":{"In":[0],"this":[1,39],"paper,":[2],"we":[3,37,55,65],"propose":[4,66],"a":[5,28],"posteriori":[6],"local":[7],"error":[8],"estimates":[9],"for":[10,26,70],"numerical":[11,58],"schemes":[12,25,43],"in":[13,45],"the":[14,24,61,71,74],"context":[15],"of":[16,73],"one-dimensional":[17],"scalar":[18],"conservation":[19],"laws.":[20],"We":[21],"first":[22],"consider":[23],"which":[27],"consistent":[29],"in-cell":[30],"entropy":[31,50],"inequality":[32],"can":[33],"be":[34],"derived.":[35],"Then":[36],"extend":[38],"result":[40],"to":[41],"second-order":[42],"written":[44],"viscous":[46],"form":[47],"satisfying":[48],"weak":[49],"inequalities.":[51],"As":[52],"an":[53,67],"illustration,":[54],"show":[56],"several":[57],"tests":[59],"on":[60],"Burgers":[62],"equation":[63],"and":[64],"adaptive":[68],"algorithm":[69],"selection":[72],"mesh.":[75]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
