{"id":"https://openalex.org/W2082961961","doi":"https://doi.org/10.1137/130926006","title":"Analysis of Operator Splitting in the Nonasymptotic Regime for Nonlinear Reaction-Diffusion Equations. Application to the Dynamics of Premixed Flames","display_name":"Analysis of Operator Splitting in the Nonasymptotic Regime for Nonlinear Reaction-Diffusion Equations. Application to the Dynamics of Premixed Flames","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2082961961","doi":"https://doi.org/10.1137/130926006","mag":"2082961961"},"language":"en","primary_location":{"id":"doi:10.1137/130926006","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130926006","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1402.1828","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112296910","display_name":"St\u00e9phane Descombes","orcid":null},"institutions":[{"id":"https://openalex.org/I4210112930","display_name":"Laboratoire Jean-Alexandre Dieudonn\u00e9","ror":"https://ror.org/0274zdr66","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I201841394","https://openalex.org/I4210112930","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"St\u00e9phane Descombes","raw_affiliation_strings":["Laboratoire Jean Alexandre Dieudonn\u00e9"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jean Alexandre Dieudonn\u00e9","institution_ids":["https://openalex.org/I4210112930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000136459","display_name":"Max Duarte","orcid":null},"institutions":[{"id":"https://openalex.org/I4210112930","display_name":"Laboratoire Jean-Alexandre Dieudonn\u00e9","ror":"https://ror.org/0274zdr66","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I201841394","https://openalex.org/I4210112930","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Max Duarte","raw_affiliation_strings":["Laboratoire Jean Alexandre Dieudonn\u00e9","Lawrence Berkeley National Laboratory [Berkeley]"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jean Alexandre Dieudonn\u00e9","institution_ids":["https://openalex.org/I4210112930"]},{"raw_affiliation_string":"Lawrence Berkeley National Laboratory [Berkeley]","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105833920","display_name":"Thierry Dumont","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thierry Dumont","raw_affiliation_strings":["Mod\u00e9lisation math\u00e9matique, calcul scientifique"],"affiliations":[{"raw_affiliation_string":"Mod\u00e9lisation math\u00e9matique, calcul scientifique","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040283430","display_name":"Fr\u00e9d\u00e9rique Laurent","orcid":"https://orcid.org/0000-0002-7365-1205"},"institutions":[{"id":"https://openalex.org/I4210127286","display_name":"Laboratoire d'\u00c9nerg\u00e9tique Mol\u00e9culaire et Macroscopique, Combustion","ror":"https://ror.org/02wy3s959","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210095849","https://openalex.org/I4210107720","https://openalex.org/I4210127286"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9rique Laurent","raw_affiliation_strings":["Laboratoire d'\u00c9nerg\u00e9tique Mol\u00e9culaire et Macroscopique, Combustion"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'\u00c9nerg\u00e9tique Mol\u00e9culaire et Macroscopique, Combustion","institution_ids":["https://openalex.org/I4210127286"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008121410","display_name":"Violaine Louvet","orcid":"https://orcid.org/0000-0002-8742-8952"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Violaine Louvet","raw_affiliation_strings":["Mod\u00e9lisation math\u00e9matique, calcul scientifique"],"affiliations":[{"raw_affiliation_string":"Mod\u00e9lisation math\u00e9matique, calcul scientifique","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055196143","display_name":"Marc Massot","orcid":"https://orcid.org/0000-0001-8823-7667"},"institutions":[{"id":"https://openalex.org/I4210127286","display_name":"Laboratoire d'\u00c9nerg\u00e9tique Mol\u00e9culaire et Macroscopique, Combustion","ror":"https://ror.org/02wy3s959","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210095849","https://openalex.org/I4210107720","https://openalex.org/I4210127286"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marc Massot","raw_affiliation_strings":["Laboratoire d'\u00c9nerg\u00e9tique Mol\u00e9culaire et Macroscopique, Combustion"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'\u00c9nerg\u00e9tique Mol\u00e9culaire et Macroscopique, Combustion","institution_ids":["https://openalex.org/I4210127286"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5112296910"],"corresponding_institution_ids":["https://openalex.org/I4210112930"],"apc_list":null,"apc_paid":null,"fwci":2.7496,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.89199553,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"52","issue":"3","first_page":"1311","last_page":"1334"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9995999932289124,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9994999766349792,"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/T10553","display_name":"Combustion and flame dynamics","score":0.9984999895095825,"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/operator-splitting","display_name":"Operator splitting","score":0.7457116842269897},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6924372911453247},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6439686417579651},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.49712756276130676},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.4760339558124542},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.45687544345855713},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.44295862317085266},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.43886762857437134},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4313701391220093},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42599648237228394},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3738372325897217},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23511269688606262},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.1680280864238739},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08330053091049194}],"concepts":[{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.7457116842269897},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6924372911453247},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6439686417579651},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.49712756276130676},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.4760339558124542},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.45687544345855713},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.44295862317085266},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.43886762857437134},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4313701391220093},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42599648237228394},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3738372325897217},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23511269688606262},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.1680280864238739},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08330053091049194},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/130926006","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130926006","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:arXiv.org:1402.1828","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1402.1828","pdf_url":"https://arxiv.org/pdf/1402.1828","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.400.1541","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.400.1541","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/83/70/89/PDF/Splitting_Descetal_Paper.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00837089v4","is_oa":true,"landing_page_url":"https://hal.science/hal-00837089","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, 2014, 52 (3), pp.1311-1334. &#x27E8;10.1137/130926006&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1402.1828","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1402.1828","pdf_url":"https://arxiv.org/pdf/1402.1828","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W85719053","https://openalex.org/W279567680","https://openalex.org/W578551519","https://openalex.org/W1592378316","https://openalex.org/W1902819800","https://openalex.org/W1971663583","https://openalex.org/W1978122310","https://openalex.org/W1979156898","https://openalex.org/W1980642013","https://openalex.org/W1985987254","https://openalex.org/W1988754720","https://openalex.org/W1990893845","https://openalex.org/W1993325724","https://openalex.org/W1993825802","https://openalex.org/W2007657466","https://openalex.org/W2012856060","https://openalex.org/W2040509377","https://openalex.org/W2044077544","https://openalex.org/W2047626766","https://openalex.org/W2049161806","https://openalex.org/W2053909454","https://openalex.org/W2060930721","https://openalex.org/W2061143699","https://openalex.org/W2062951693","https://openalex.org/W2068452529","https://openalex.org/W2068650655","https://openalex.org/W2071540247","https://openalex.org/W2079477617","https://openalex.org/W2082390516","https://openalex.org/W2083549357","https://openalex.org/W2092400970","https://openalex.org/W2093063406","https://openalex.org/W2109866862","https://openalex.org/W2113597488","https://openalex.org/W2119181847","https://openalex.org/W2139219363","https://openalex.org/W2317460055","https://openalex.org/W2525500864","https://openalex.org/W2947056241","https://openalex.org/W2969232873","https://openalex.org/W3099454971","https://openalex.org/W4205629667","https://openalex.org/W4254432473","https://openalex.org/W4292329038","https://openalex.org/W4293515545"],"related_works":["https://openalex.org/W2318982644","https://openalex.org/W2290544825","https://openalex.org/W2952002389","https://openalex.org/W24076686","https://openalex.org/W2791671051","https://openalex.org/W1539544820","https://openalex.org/W4226416379","https://openalex.org/W2126858039","https://openalex.org/W2126481471","https://openalex.org/W1975406625"],"abstract_inverted_index":{"In":[0,62],"this":[1],"paper":[2],"we":[3],"mathematically":[4],"characterize":[5],"through":[6],"a":[7,63,68,75,111,126,166,184],"Lie":[8,141],"formalism":[9,142],"the":[10,24,36,46,54,71,89,119,147,160,171,195,208],"local":[11,176],"errors":[12,124],"induced":[13],"by":[14,139],"operator":[15,56],"splitting":[16,37,79,123],"when":[17,35,57],"solving":[18],"nonlinear":[19,90,129],"reaction-diffusion":[20],"equations,":[21],"especially":[22],"in":[23,33,88,159,194],"nonasymptotic":[25,28],"regime.":[26],"The":[27,150],"regime":[29,199],"is":[30,40,156],"often":[31],"attained":[32],"practice":[34],"time":[38,80,86],"step":[39,114],"much":[41,185],"larger":[42],"than":[43],"some":[44],"of":[45,65,70,77,122,146,152,162,173],"scales":[47,87],"associated":[48,100],"with":[49,101,200],"either":[50],"source":[51,91],"terms":[52],"or":[53],"diffusion":[55],"large":[58,78,102],"gradients":[59,103],"are":[60],"present.":[61],"series":[64],"previous":[66],"works":[67],"reduction":[69],"asymptotic":[72],"orders":[73],"for":[74,105,131,206],"range":[76],"steps":[81],"related":[82,189],"to":[83,190],"very":[84],"short":[85],"term":[92],"has":[93],"been":[94],"studied,":[95],"as":[96,98],"well":[97],"that":[99],"but":[104],"linearized":[106],"equations.":[107],"This":[108],"study":[109,211],"provides":[110,212],"key":[112],"theoretical":[113,154,210],"forward":[115],"since":[116],"it":[117],"characterizes":[118],"numerical":[120,164],"behavior":[121],"within":[125],"more":[127,186],"general":[128],"framework,":[130],"which":[132,207],"new":[133],"error":[134,177],"estimates":[135,178],"can":[136,179],"be":[137,180],"derived":[138],"coupling":[140],"and":[143,183,203],"regularizing":[144],"effects":[145],"heat":[148],"equation.":[149],"validity":[151],"these":[153],"results":[155],"then":[157],"assessed":[158],"framework":[161],"two":[163],"applications:":[165],"Kolmogorov--Petrovskii--Piskunov-type":[167],"reaction":[168],"wave":[169],"where":[170],"influence":[172],"stiffness":[174],"on":[175],"thoroughly":[181],"investigated":[182],"complex":[187,201],"problem,":[188],"premixed":[191],"flame":[192],"dynamics":[193],"low":[196],"Mach":[197],"number":[198],"chemistry":[202],"detailed":[204],"transport,":[205],"present":[209],"relevant":[213],"insights.":[214]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
