{"id":"https://openalex.org/W2051269517","doi":"https://doi.org/10.1137/110859282","title":"A Framework for Robust A Posteriori Error Control in Unsteady Nonlinear Advection-Diffusion Problems","display_name":"A Framework for Robust A Posteriori Error Control in Unsteady Nonlinear Advection-Diffusion Problems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2051269517","doi":"https://doi.org/10.1137/110859282","mag":"2051269517"},"language":"en","primary_location":{"id":"doi:10.1137/110859282","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110859282","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/A5023276584","display_name":"V\u00edt Dolej\u0161\u00ed","orcid":"https://orcid.org/0000-0001-6356-934X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V\u00edt Dolej\u0161\u00ed","raw_affiliation_strings":["Department of Numerical Mathematics (Czech Republic)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Numerical Mathematics (Czech Republic)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061539614","display_name":"Alexandre Ern","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alexandre Ern","raw_affiliation_strings":["CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020083948","display_name":"Martin Vohral\u0131\u0301k","orcid":"https://orcid.org/0000-0002-8838-7689"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Vohral\u00edk","raw_affiliation_strings":["POMDAPI - Environmental Modeling, Optimization and Programming Models (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"POMDAPI - Environmental Modeling, Optimization and Programming Models (France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.9963,"has_fulltext":true,"cited_by_count":38,"citation_normalized_percentile":{"value":0.96522229,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"51","issue":"2","first_page":"773","last_page":"793"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.998199999332428,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7282308340072632},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6592693328857422},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5886284112930298},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5678834915161133},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5409456491470337},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5361217260360718},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5256313681602478},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.49718406796455383},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.43295055627822876},{"id":"https://openalex.org/keywords/space-time","display_name":"Space time","score":0.4194672703742981},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4144042134284973},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38185960054397583},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16743895411491394},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.16100355982780457},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1054459810256958}],"concepts":[{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7282308340072632},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6592693328857422},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5886284112930298},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5678834915161133},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5409456491470337},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5361217260360718},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5256313681602478},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.49718406796455383},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.43295055627822876},{"id":"https://openalex.org/C96402334","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Space time","level":2,"score":0.4194672703742981},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4144042134284973},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38185960054397583},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16743895411491394},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.16100355982780457},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1054459810256958},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/110859282","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110859282","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-00652979v2","is_oa":false,"landing_page_url":"https://hal.science/hal-00652979","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2013, 51 (2), pp.773-793. &#x27E8;10.1137/110859282&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.47999998927116394}],"awards":[{"id":"https://openalex.org/G2955613702","display_name":null,"funder_award_id":"201/08/0012","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320322219","display_name":"IFP Energies Nouvelles","ror":"https://ror.org/03gcbhc33"},{"id":"https://openalex.org/F4320322760","display_name":"Institut de Radioprotection et de S\u00dbret\u00e9 Nucl\u00e9aire","ror":"https://ror.org/01ha22c77"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320323731","display_name":"Bureau de Recherches G\u00e9ologiques et Mini\u00e8res","ror":"https://ror.org/05hnb7x64"},{"id":"https://openalex.org/F4320324081","display_name":"Agence Nationale pour la Gestion des D\u00e9chets Radioactifs","ror":"https://ror.org/04qkhgw46"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W100357283","https://openalex.org/W1971606961","https://openalex.org/W1972684149","https://openalex.org/W1975505063","https://openalex.org/W1985988195","https://openalex.org/W1995315845","https://openalex.org/W2006443697","https://openalex.org/W2008428857","https://openalex.org/W2008683313","https://openalex.org/W2015102272","https://openalex.org/W2015788535","https://openalex.org/W2016535570","https://openalex.org/W2023111075","https://openalex.org/W2029725158","https://openalex.org/W2034290095","https://openalex.org/W2040477085","https://openalex.org/W2061174143","https://openalex.org/W2064265943","https://openalex.org/W2067951086","https://openalex.org/W2069591987","https://openalex.org/W2072973709","https://openalex.org/W2074006304","https://openalex.org/W2081396510","https://openalex.org/W2086501907","https://openalex.org/W2087270837","https://openalex.org/W2103705455","https://openalex.org/W2153299448","https://openalex.org/W2154523804","https://openalex.org/W2562668947"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2366350639","https://openalex.org/W2028455732","https://openalex.org/W2163017860","https://openalex.org/W4295815745","https://openalex.org/W2953079798","https://openalex.org/W1969674427","https://openalex.org/W3092754077","https://openalex.org/W2981222881","https://openalex.org/W235193856"],"abstract_inverted_index":{"We":[0,144],"derive":[1],"a":[2,5,21,38,53,65,106,121],"framework":[3,119],"for":[4,33,105,150],"posteriori":[6],"error":[7,35,112],"estimates":[8],"in":[9,37,59,156,162],"unsteady,":[10],"nonlinear,":[11],"possibly":[12],"degenerate,":[13],"advection-diffusion":[14],"problems.":[15],"Our":[16],"estimators":[17],"are":[18,27,31],"based":[19],"on":[20],"space-time":[22,39,129],"equilibrated":[23],"flux":[24],"reconstruction":[25],"and":[26,47,67,88,90,95,99,132,158],"locally":[28],"computable.":[29],"They":[30],"derived":[32],"the":[34,45,111,118,137,151,159,167],"measured":[36],"mesh-dependent":[40],"dual":[41],"norm":[42],"stemming":[43],"from":[44],"problem":[46],"meshes":[48],"at":[49],"hand":[50],"augmented":[51],"by":[52],"jump":[54],"seminorm":[55],"measuring":[56],"possible":[57],"nonconformities":[58],"space.":[60],"Owing":[61],"to":[62,80,116,120,141,147],"this":[63,149],"choice,":[64],"guaranteed":[66],"globally":[68],"efficient":[69],"upper":[70,108],"bound":[71,109],"is":[72,102],"achieved,":[73],"as":[74,76],"well":[75],"robustness":[77],"with":[78],"respect":[79],"nonlinearities,":[81],"advection":[82],"dominance,":[83],"domain":[84],"size,":[85],"final":[86],"time,":[87],"absolute":[89],"relative":[91],"size":[92],"of":[93,110,136],"space":[94,157],"time":[96],"steps.":[97],"Local-in-time":[98],"in-space":[100],"efficiency":[101],"also":[103],"shown":[104],"localized":[107],"measure.":[113],"In":[114],"order":[115],"apply":[117],"given":[122],"numerical":[123],"method,":[124],"two":[125],"simple":[126],"conditions,":[127],"local":[128],"mass":[130],"conservation":[131],"an":[133],"approximation":[134],"property":[135],"reconstructed":[138],"fluxes,":[139],"need":[140],"be":[142],"verified.":[143],"show":[145],"how":[146],"do":[148],"interior-penalty":[152],"discontinuous":[153],"Galerkin":[154],"method":[155],"Crank--Nicolson":[160],"scheme":[161],"time.":[163],"Numerical":[164],"experiments":[165],"illustrate":[166],"theory.":[168]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
