{"id":"https://openalex.org/W4306688622","doi":"https://doi.org/10.1137/21m1464841","title":"An Introductory Review on A Posteriori Error Estimation in Finite Element Computations","display_name":"An Introductory Review on A Posteriori Error Estimation in Finite Element Computations","publication_year":2023,"publication_date":"2023-11-01","ids":{"openalex":"https://openalex.org/W4306688622","doi":"https://doi.org/10.1137/21m1464841"},"language":"en","primary_location":{"id":"doi:10.1137/21m1464841","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1464841","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/pdf/2110.02160","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066792673","display_name":"Ludovic Chamoin","orcid":"https://orcid.org/0000-0002-8361-0757"},"institutions":[{"id":"https://openalex.org/I11559806","display_name":"\u00c9cole Normale Sup\u00e9rieure Paris-Saclay","ror":"https://ror.org/00hx6zz33","country_code":"FR","type":"education","lineage":["https://openalex.org/I11559806","https://openalex.org/I277688954"]},{"id":"https://openalex.org/I185839726","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266","country_code":"FR","type":"education","lineage":["https://openalex.org/I185839726"]},{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]},{"id":"https://openalex.org/I4210150317","display_name":"Laboratoire de Biologie et Pharmacologie Appliqu\u00e9e","ror":"https://ror.org/03njrcx45","country_code":"FR","type":"facility","lineage":["https://openalex.org/I11559806","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210096427","https://openalex.org/I4210150317"]},{"id":"https://openalex.org/I4387154615","display_name":"Laboratoire de M\u00e9canique Paris-Saclay","ror":"https://ror.org/01jv2ft75","country_code":"FR","type":"facility","lineage":["https://openalex.org/I11559806","https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4387154615"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ludovic Chamoin","raw_affiliation_strings":["ENS Paris Saclay - Ecole Normale Sup\u00e9rieure  Paris-Saclay (4 avenue des Sciences, 91190 Gif-sur-Yvette - France)","IUF - Institut universitaire de France (Maison des Universit\u00e9s 103 Boulevard Saint-Michel 75005 Paris - France)","LMPS - Laboratoire de M\u00e9canique Paris-Saclay (4 avenue des sciences / 8-10 rue Joliot Curie, 91190 Gif-sur-Yvette - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ENS Paris Saclay - Ecole Normale Sup\u00e9rieure  Paris-Saclay (4 avenue des Sciences, 91190 Gif-sur-Yvette - France)","institution_ids":["https://openalex.org/I11559806","https://openalex.org/I29607241","https://openalex.org/I4210150317"]},{"raw_affiliation_string":"IUF - Institut universitaire de France (Maison des Universit\u00e9s 103 Boulevard Saint-Michel 75005 Paris - France)","institution_ids":["https://openalex.org/I185839726"]},{"raw_affiliation_string":"LMPS - Laboratoire de M\u00e9canique Paris-Saclay (4 avenue des sciences / 8-10 rue Joliot Curie, 91190 Gif-sur-Yvette - France)","institution_ids":["https://openalex.org/I4387154615"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108100026","display_name":"Fr\u00e9d\u00e9ric Legoll","orcid":"https://orcid.org/0000-0002-2334-5058"},"institutions":[{"id":"https://openalex.org/I142631665","display_name":"\u00c9cole nationale des ponts et chauss\u00e9es","ror":"https://ror.org/02nwvxz07","country_code":"FR","type":"education","lineage":["https://openalex.org/I142631665","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Legoll","raw_affiliation_strings":["MATHERIALS - MATHematics for MatERIALS (France)","Multi-\u00e9chelle - Mod\u00e9lisation et exp\u00e9rimentation multi-\u00e9chelle pour les solides h\u00e9t\u00e9rog\u00e8nes (\u00c9cole des Ponts ParisTech, 6-8 avenue Blaise Pascal - Cit\u00e9 Descartes - Champs-sur-Marne, 77455 Marne-la-Vall\u00e9e cedex 2 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MATHERIALS - MATHematics for MatERIALS (France)","institution_ids":[]},{"raw_affiliation_string":"Multi-\u00e9chelle - Mod\u00e9lisation et exp\u00e9rimentation multi-\u00e9chelle pour les solides h\u00e9t\u00e9rog\u00e8nes (\u00c9cole des Ponts ParisTech, 6-8 avenue Blaise Pascal - Cit\u00e9 Descartes - Champs-sur-Marne, 77455 Marne-la-Vall\u00e9e cedex 2 - France)","institution_ids":["https://openalex.org/I142631665"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.4054,"has_fulltext":true,"cited_by_count":33,"citation_normalized_percentile":{"value":0.9756312,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"65","issue":"4","first_page":"963","last_page":"1028"},"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":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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/T10514","display_name":"Numerical methods in engineering","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6165282726287842},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6063040494918823},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5524100065231323},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5469510555267334},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.5425861477851868},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5381314158439636},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.505558967590332},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.49279049038887024},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4887351989746094},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4678875505924225},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4261137843132019},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39364564418792725},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37272125482559204},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33493900299072266},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09192454814910889}],"concepts":[{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6165282726287842},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6063040494918823},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5524100065231323},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5469510555267334},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.5425861477851868},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5381314158439636},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.505558967590332},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.49279049038887024},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4887351989746094},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4678875505924225},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4261137843132019},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39364564418792725},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37272125482559204},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33493900299072266},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09192454814910889},{"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},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/21m1464841","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1464841","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03368356v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03368356","pdf_url":"http://arxiv.org/pdf/2110.02160","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 Review, 2023, 65 (4), pp.963-1028. ⟨10.1137/21M1464841⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03368356v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03368356","pdf_url":"http://arxiv.org/pdf/2110.02160","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 Review, 2023, 65 (4), pp.963-1028. ⟨10.1137/21M1464841⟩","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3014976319","display_name":null,"funder_award_id":"N00014-20-1-2691","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G6391341468","display_name":null,"funder_award_id":"FA8655-20-1-7043","funder_id":"https://openalex.org/F4320338503","funder_display_name":"European Office of Aerospace Research and Development"},{"id":"https://openalex.org/G8006577219","display_name":null,"funder_award_id":"N00014-20","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338503","display_name":"European Office of Aerospace Research and Development","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4306688622.pdf","grobid_xml":"https://content.openalex.org/works/W4306688622.grobid-xml"},"referenced_works_count":252,"referenced_works":["https://openalex.org/W100357283","https://openalex.org/W182469685","https://openalex.org/W184188664","https://openalex.org/W253824085","https://openalex.org/W280547473","https://openalex.org/W589524848","https://openalex.org/W592911714","https://openalex.org/W624819622","https://openalex.org/W653136046","https://openalex.org/W1573186872","https://openalex.org/W1601728065","https://openalex.org/W1603402123","https://openalex.org/W1667557491","https://openalex.org/W1787925643","https://openalex.org/W1793171420","https://openalex.org/W1924336391","https://openalex.org/W1927560861","https://openalex.org/W1963959271","https://openalex.org/W1965373282","https://openalex.org/W1965818487","https://openalex.org/W1966388474","https://openalex.org/W1966496196","https://openalex.org/W1966525999","https://openalex.org/W1970091858","https://openalex.org/W1971606961","https://openalex.org/W1972684149","https://openalex.org/W1973286520","https://openalex.org/W1973710316","https://openalex.org/W1976200775","https://openalex.org/W1976435787","https://openalex.org/W1977130752","https://openalex.org/W1977250902","https://openalex.org/W1978646283","https://openalex.org/W1979122337","https://openalex.org/W1979633028","https://openalex.org/W1980377066","https://openalex.org/W1980964769","https://openalex.org/W1981327633","https://openalex.org/W1983083525","https://openalex.org/W1985422345","https://openalex.org/W1985629301","https://openalex.org/W1985988195","https://openalex.org/W1986514168","https://openalex.org/W1987306140","https://openalex.org/W1987865080","https://openalex.org/W1989594010","https://openalex.org/W1991045865","https://openalex.org/W1992522720","https://openalex.org/W1992628806","https://openalex.org/W1992629186","https://openalex.org/W1993204688","https://openalex.org/W1994336408","https://openalex.org/W1996140937","https://openalex.org/W1997703844","https://openalex.org/W1997749848","https://openalex.org/W1998050976","https://openalex.org/W1999581803","https://openalex.org/W2001268006","https://openalex.org/W2001984348","https://openalex.org/W2004262512","https://openalex.org/W2005152402","https://openalex.org/W2005259457","https://openalex.org/W2007289139","https://openalex.org/W2008428857","https://openalex.org/W2008435923","https://openalex.org/W2009171873","https://openalex.org/W2009607034","https://openalex.org/W2009628646","https://openalex.org/W2009985306","https://openalex.org/W2010431816","https://openalex.org/W2010637116","https://openalex.org/W2011203316","https://openalex.org/W2011884938","https://openalex.org/W2012460653","https://openalex.org/W2016628818","https://openalex.org/W2016930521","https://openalex.org/W2017346595","https://openalex.org/W2018233090","https://openalex.org/W2018914564","https://openalex.org/W2019057877","https://openalex.org/W2019884679","https://openalex.org/W2020292714","https://openalex.org/W2020854958","https://openalex.org/W2021578418","https://openalex.org/W2024029918","https://openalex.org/W2025273066","https://openalex.org/W2025769367","https://openalex.org/W2026757688","https://openalex.org/W2027619967","https://openalex.org/W2028104041","https://openalex.org/W2028526482","https://openalex.org/W2029849785","https://openalex.org/W2030230799","https://openalex.org/W2033698269","https://openalex.org/W2034100225","https://openalex.org/W2034290095","https://openalex.org/W2037574639","https://openalex.org/W2037868675","https://openalex.org/W2039924562","https://openalex.org/W2041896318","https://openalex.org/W2042199582","https://openalex.org/W2042426282","https://openalex.org/W2044892973","https://openalex.org/W2045214757","https://openalex.org/W2046300718","https://openalex.org/W2050111551","https://openalex.org/W2050285722","https://openalex.org/W2050520071","https://openalex.org/W2051775663","https://openalex.org/W2051889472","https://openalex.org/W2052686349","https://openalex.org/W2052690618","https://openalex.org/W2052813513","https://openalex.org/W2052848091","https://openalex.org/W2053162126","https://openalex.org/W2056027508","https://openalex.org/W2057849496","https://openalex.org/W2059848088","https://openalex.org/W2059951022","https://openalex.org/W2060131826","https://openalex.org/W2060365416","https://openalex.org/W2060383701","https://openalex.org/W2060866894","https://openalex.org/W2062360619","https://openalex.org/W2063345898","https://openalex.org/W2065438814","https://openalex.org/W2065468055","https://openalex.org/W2066031933","https://openalex.org/W2066927514","https://openalex.org/W2070033465","https://openalex.org/W2070623505","https://openalex.org/W2072811159","https://openalex.org/W2074623661","https://openalex.org/W2075294054","https://openalex.org/W2075653737","https://openalex.org/W2076956302","https://openalex.org/W2078125003","https://openalex.org/W2079318234","https://openalex.org/W2081954723","https://openalex.org/W2082334670","https://openalex.org/W2082786362","https://openalex.org/W2083027300","https://openalex.org/W2084743165","https://openalex.org/W2084862534","https://openalex.org/W2084949742","https://openalex.org/W2085739550","https://openalex.org/W2085882457","https://openalex.org/W2087263350","https://openalex.org/W2088831497","https://openalex.org/W2089757800","https://openalex.org/W2090606685","https://openalex.org/W2092185402","https://openalex.org/W2092360659","https://openalex.org/W2094274747","https://openalex.org/W2095270108","https://openalex.org/W2097626286","https://openalex.org/W2101274463","https://openalex.org/W2102753028","https://openalex.org/W2103705455","https://openalex.org/W2104225554","https://openalex.org/W2104426156","https://openalex.org/W2105154179","https://openalex.org/W2105729768","https://openalex.org/W2105966434","https://openalex.org/W2106182283","https://openalex.org/W2106400106","https://openalex.org/W2106678274","https://openalex.org/W2107813568","https://openalex.org/W2108285310","https://openalex.org/W2108389905","https://openalex.org/W2109919892","https://openalex.org/W2118800976","https://openalex.org/W2119590936","https://openalex.org/W2120331018","https://openalex.org/W2121560838","https://openalex.org/W2121985173","https://openalex.org/W2122074662","https://openalex.org/W2122461891","https://openalex.org/W2125861594","https://openalex.org/W2126312292","https://openalex.org/W2128497093","https://openalex.org/W2129479945","https://openalex.org/W2130350269","https://openalex.org/W2131660612","https://openalex.org/W2131676152","https://openalex.org/W2132719389","https://openalex.org/W2133147107","https://openalex.org/W2134154407","https://openalex.org/W2134247452","https://openalex.org/W2137332760","https://openalex.org/W2137365186","https://openalex.org/W2137620714","https://openalex.org/W2137664537","https://openalex.org/W2138564303","https://openalex.org/W2143518999","https://openalex.org/W2144181355","https://openalex.org/W2144451871","https://openalex.org/W2148639620","https://openalex.org/W2150140956","https://openalex.org/W2152113173","https://openalex.org/W2155395549","https://openalex.org/W2157121531","https://openalex.org/W2158291708","https://openalex.org/W2162992695","https://openalex.org/W2167521757","https://openalex.org/W2168438989","https://openalex.org/W2170343812","https://openalex.org/W2277348547","https://openalex.org/W2289792662","https://openalex.org/W2300243767","https://openalex.org/W2321310861","https://openalex.org/W2324136870","https://openalex.org/W2414524077","https://openalex.org/W2467444363","https://openalex.org/W2470116742","https://openalex.org/W2487440882","https://openalex.org/W2495211843","https://openalex.org/W2499367340","https://openalex.org/W2505585705","https://openalex.org/W2510475660","https://openalex.org/W2538438809","https://openalex.org/W2551508900","https://openalex.org/W2566906166","https://openalex.org/W2573993005","https://openalex.org/W2607775705","https://openalex.org/W2673889020","https://openalex.org/W2751317846","https://openalex.org/W2752189732","https://openalex.org/W2754136983","https://openalex.org/W2776142461","https://openalex.org/W2782548004","https://openalex.org/W2907468423","https://openalex.org/W2912587611","https://openalex.org/W2947304844","https://openalex.org/W2952600621","https://openalex.org/W2963066470","https://openalex.org/W2997217435","https://openalex.org/W3022640995","https://openalex.org/W3022880066","https://openalex.org/W3024741178","https://openalex.org/W3033830016","https://openalex.org/W3043267565","https://openalex.org/W3128885210","https://openalex.org/W3139157454","https://openalex.org/W3196926221","https://openalex.org/W3204708751","https://openalex.org/W4210300254","https://openalex.org/W4230524683","https://openalex.org/W4239704419","https://openalex.org/W4241656903","https://openalex.org/W4247375400","https://openalex.org/W4292079189"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2610540941","https://openalex.org/W2362625355","https://openalex.org/W2371228119"],"abstract_inverted_index":{"This":[0],"article":[1],"is":[2,51],"a":[3,12,41,55,58,152],"review":[4,50],"of":[5,27,48,61,69,98,122],"basic":[6],"concepts":[7],"and":[8,29,83,92],"tools":[9],"devoted":[10],"to":[11,52,130],"posteriori":[13],"error":[14,77,102,105,113,118],"estimation":[15,97,114],"for":[16,95],"problems":[17],"solved":[18],"with":[19],"the":[20,25,67,96,99,104,117,127],"finite":[21],"element":[22],"method.":[23],"For":[24],"sake":[26],"simplicity":[28],"clarity,":[30],"we":[31],"mostly":[32],"focus":[33],"on":[34,73,119,151],"linear":[35,153],"elliptic":[36],"diffusion":[37],"problems,":[38],"approximated":[39],"by":[40],"conforming":[42],"numerical":[43,132,149],"discretization.":[44],"The":[45],"main":[46],"goal":[47],"this":[49],"present":[53],"in":[54,106,156],"unified":[56],"manner":[57],"large":[59],"set":[60],"powerful":[62],"verification":[63],"methods,":[64,89,91,133],"centered":[65],"around":[66],"concept":[68,75],"equilibrium.":[70],"Methods":[71],"based":[72],"that":[74,79],"provide":[76,146],"bounds":[78],"are":[80],"fully":[81],"computable":[82],"mathematically":[84],"certified.":[85],"We":[86,124,144],"discuss":[87],"recovery":[88],"residual":[90],"duality-based":[93],"methods":[94],"whole":[100],"solution":[101],"(i.e.,":[103],"energy":[107],"norm),":[108],"as":[109,111,134,136],"well":[110,135],"goal-oriented":[112],"(to":[115],"assess":[116],"specific":[120],"quantities":[121],"interest).":[123],"briefly":[125],"survey":[126],"possible":[128],"extensions":[129],"nonconforming":[131],"more":[137],"complex":[138],"(e.g.,":[139],"nonlinear":[140],"or":[141],"time-dependent)":[142],"problems.":[143],"also":[145],"some":[147],"illustrating":[148],"examples":[150],"elasticity":[154],"problem":[155],"three":[157],"dimensions.":[158]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":11}],"updated_date":"2026-08-19T15:00:24.278416","created_date":"2022-10-19T00:00:00"}