{"id":"https://openalex.org/W2979360014","doi":"https://doi.org/10.1007/s00211-019-01075-1","title":"Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems","display_name":"Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems","publication_year":2019,"publication_date":"2019-10-10","ids":{"openalex":"https://openalex.org/W2979360014","doi":"https://doi.org/10.1007/s00211-019-01075-1","mag":"2979360014"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-019-01075-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-019-01075-1","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5001132837","display_name":"Difeng Cai","orcid":"https://orcid.org/0000-0001-9482-6425"},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Difeng Cai","raw_affiliation_strings":["Department of Mathematics, Emory University, 201 Dowman Drive, Atlanta, GA, 30322, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Emory University, 201 Dowman Drive, Atlanta, GA, 30322, USA","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023481731","display_name":"Zhiqiang Cai","orcid":"https://orcid.org/0000-0002-3775-7248"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhiqiang Cai","raw_affiliation_strings":["Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN, 47907-2067, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN, 47907-2067, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100415439","display_name":"Shun Zhang","orcid":"https://orcid.org/0000-0002-5826-8611"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Shun Zhang","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong SAR, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong SAR, China","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023481731"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.3535,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.79620307,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"144","issue":"1","first_page":"1","last_page":"21"},"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":1.0,"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":1.0,"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":0.9957000017166138,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9837999939918518,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8097681403160095},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7602027654647827},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7546625137329102},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7049170732498169},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.636548638343811},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5734663605690002},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.541985809803009},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5090115070343018},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.49903059005737305},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4563705027103424},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4355516731739044},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.329135000705719},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1425846815109253},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08727854490280151}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8097681403160095},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7602027654647827},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7546625137329102},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7049170732498169},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.636548638343811},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5734663605690002},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.541985809803009},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5090115070343018},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.49903059005737305},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4563705027103424},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4355516731739044},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.329135000705719},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1425846815109253},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08727854490280151},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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":1,"locations":[{"id":"doi:10.1007/s00211-019-01075-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-019-01075-1","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W46814297","https://openalex.org/W253824085","https://openalex.org/W592368443","https://openalex.org/W592911714","https://openalex.org/W1523673167","https://openalex.org/W1524015806","https://openalex.org/W1597196612","https://openalex.org/W1966388474","https://openalex.org/W1971606961","https://openalex.org/W1980377066","https://openalex.org/W1995404822","https://openalex.org/W1998674934","https://openalex.org/W1998771439","https://openalex.org/W2004434279","https://openalex.org/W2007809587","https://openalex.org/W2020854958","https://openalex.org/W2033698269","https://openalex.org/W2034700720","https://openalex.org/W2039924562","https://openalex.org/W2044166686","https://openalex.org/W2044892973","https://openalex.org/W2046300718","https://openalex.org/W2055009689","https://openalex.org/W2154523804","https://openalex.org/W2155395549","https://openalex.org/W2155768256","https://openalex.org/W2505585705","https://openalex.org/W2562668947","https://openalex.org/W2803872738","https://openalex.org/W2963610501","https://openalex.org/W6602301541"],"related_works":["https://openalex.org/W4245953108","https://openalex.org/W2033785827","https://openalex.org/W2264690077","https://openalex.org/W2808231882","https://openalex.org/W4318824563","https://openalex.org/W2394496373","https://openalex.org/W2311985367","https://openalex.org/W2953763369","https://openalex.org/W2097626286","https://openalex.org/W2079924178"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}