{"id":"https://openalex.org/W815078598","doi":"https://doi.org/10.1137/15m1029886","title":"Error Estimate for Time-Explicit Finite Volume Approximation of Strong Solutions to Systems of Conservation Laws","display_name":"Error Estimate for Time-Explicit Finite Volume Approximation of Strong Solutions to Systems of Conservation Laws","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W815078598","doi":"https://doi.org/10.1137/15m1029886","mag":"815078598"},"language":"en","primary_location":{"id":"doi:10.1137/15m1029886","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1029886","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":true,"oa_status":"green","oa_url":"https://hal.science/hal-00798287","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035995124","display_name":"Cl\u00e9ment Canc\u00e8s","orcid":"https://orcid.org/0000-0002-7682-1695"},"institutions":[{"id":"https://openalex.org/I4210101304","display_name":"Prediction Systems (United States)","ror":"https://ror.org/01abzsb47","country_code":"US","type":"company","lineage":["https://openalex.org/I4210101304"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Cl\u00e9ment Canc\u00e8s","raw_affiliation_strings":["Reliable numerical approximations of dissipative systems"],"affiliations":[{"raw_affiliation_string":"Reliable numerical approximations of dissipative systems","institution_ids":["https://openalex.org/I4210101304"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081175207","display_name":"H\u00e9l\u00e8ne Mathis","orcid":"https://orcid.org/0000-0003-3340-4565"},"institutions":[{"id":"https://openalex.org/I4210153365","display_name":"Laboratoire de Math\u00e9matiques Jean Leray","ror":"https://ror.org/04g1hjn96","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210153365","https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"H\u00e9l\u00e8ne Mathis","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques Jean Leray"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Jean Leray","institution_ids":["https://openalex.org/I4210153365"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061520557","display_name":"Nicolas Seguin","orcid":"https://orcid.org/0000-0001-7783-9849"},"institutions":[{"id":"https://openalex.org/I4210153365","display_name":"Laboratoire de Math\u00e9matiques Jean Leray","ror":"https://ror.org/04g1hjn96","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210153365","https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Seguin","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques Jean Leray"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Jean Leray","institution_ids":["https://openalex.org/I4210153365"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035995124"],"corresponding_institution_ids":["https://openalex.org/I4210101304"],"apc_list":null,"apc_paid":null,"fwci":2.1277,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.84543288,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"54","issue":"2","first_page":"1263","last_page":"1287"},"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":0.9979000091552734,"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":0.8600504398345947},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7609307765960693},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.7204673290252686},{"id":"https://openalex.org/keywords/numerical-approximation","display_name":"Numerical approximation","score":0.639011025428772},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.6111648678779602},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6022733449935913},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5811303853988647},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.545864999294281},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.5277358293533325},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4925740361213684},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.46351730823516846},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4271852970123291},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4152892231941223},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3417835235595703},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14873462915420532},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.09424713253974915},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08314657211303711}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.8600504398345947},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7609307765960693},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.7204673290252686},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.639011025428772},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.6111648678779602},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6022733449935913},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5811303853988647},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.545864999294281},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.5277358293533325},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4925740361213684},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.46351730823516846},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4271852970123291},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4152892231941223},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3417835235595703},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14873462915420532},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.09424713253974915},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08314657211303711},{"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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/15m1029886","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1029886","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:HAL:hal-00798287v3","is_oa":true,"landing_page_url":"https://hal.science/hal-00798287","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2016, 54 (2), pp.1263-1287. ⟨10.1137/15M1029886⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00798287v3","is_oa":true,"landing_page_url":"https://hal.science/hal-00798287","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2016, 54 (2), pp.1263-1287. ⟨10.1137/15M1029886⟩","raw_type":"Journal articles"},"sustainable_development_goals":[{"score":0.7400000095367432,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320323400","display_name":"Universit\u00e9 Pierre et Marie Curie","ror":"https://ror.org/02en5vm52"},{"id":"https://openalex.org/F4320323911","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W277149201","https://openalex.org/W1580248330","https://openalex.org/W1863894199","https://openalex.org/W1964672341","https://openalex.org/W1969819994","https://openalex.org/W1970852400","https://openalex.org/W1972924431","https://openalex.org/W1978337303","https://openalex.org/W1978519980","https://openalex.org/W1980520313","https://openalex.org/W1984735519","https://openalex.org/W1985969525","https://openalex.org/W1987468766","https://openalex.org/W1990596161","https://openalex.org/W1996627141","https://openalex.org/W1997541771","https://openalex.org/W2003044633","https://openalex.org/W2005912733","https://openalex.org/W2011669849","https://openalex.org/W2023113756","https://openalex.org/W2039093209","https://openalex.org/W2040415781","https://openalex.org/W2042118059","https://openalex.org/W2043057066","https://openalex.org/W2043581458","https://openalex.org/W2043761137","https://openalex.org/W2044000857","https://openalex.org/W2044846554","https://openalex.org/W2047742176","https://openalex.org/W2060976754","https://openalex.org/W2072226973","https://openalex.org/W2084184588","https://openalex.org/W2090386503","https://openalex.org/W2093115163","https://openalex.org/W2094923258","https://openalex.org/W2112548197","https://openalex.org/W2129822331","https://openalex.org/W3099192173","https://openalex.org/W4231817347","https://openalex.org/W4233070363","https://openalex.org/W4245820193","https://openalex.org/W4247342202"],"related_works":["https://openalex.org/W2768028474","https://openalex.org/W2951681477","https://openalex.org/W3121454024","https://openalex.org/W2081687577","https://openalex.org/W4386090364","https://openalex.org/W2727523369","https://openalex.org/W2153347081","https://openalex.org/W171329062","https://openalex.org/W2038558816","https://openalex.org/W93394153"],"abstract_inverted_index":{"We":[0,15],"study":[1],"the":[2,38,49,63,67,71],"finite":[3,76],"volume":[4,77],"approximation":[5,51],"of":[6,12,37],"strong":[7,72],"solutions":[8],"to":[9,43,86],"nonlinear":[10],"systems":[11],"conservation":[13],"laws.":[14],"focus":[16],"on":[17,20],"time-explicit":[18],"schemes":[19],"unstructured":[21],"meshes,":[22],"with":[23],"entropy":[24,30,69],"satisfying":[25],"numerical":[26,29,50],"fluxes.":[27],"The":[28,79],"dissipation":[31],"is":[32],"quantified":[33],"at":[34],"each":[35],"interface":[36],"mesh,":[39],"which":[40],"enables":[41],"us":[42],"prove":[44],"a":[45,53,87],"weak-$BV$":[46],"estimate":[47,90],"for":[48],"under":[52,93],"strengthened":[54,95],"CFL":[55,96],"condition.":[56,97],"Then":[57],"we":[58],"derive":[59],"error":[60,80],"estimates":[61],"in":[62,91],"multidimensional":[64],"case,":[65],"using":[66],"relative":[68],"between":[70],"solution":[73],"and":[74],"its":[75],"approximation.":[78],"terms":[81],"are":[82],"carefully":[83],"studied,":[84],"leading":[85],"classical":[88],"$\\mathcal{O}(h^{1/4})$":[89],"$L^2$":[92],"this":[94]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}