{"id":"https://openalex.org/W2048248082","doi":"https://doi.org/10.1137/s0036142901398751","title":"Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids","display_name":"Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2048248082","doi":"https://doi.org/10.1137/s0036142901398751","mag":"2048248082"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142901398751","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901398751","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/A5073296480","display_name":"Randolph E. Bank","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Randolph E. Bank","raw_affiliation_strings":["University of California at San Diego"],"affiliations":[{"raw_affiliation_string":"University of California at San Diego","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101494424","display_name":"Jinchao Xu","orcid":"https://orcid.org/0009-0004-4132-0227"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jinchao Xu","raw_affiliation_strings":["Mathematics"],"affiliations":[{"raw_affiliation_string":"Mathematics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073296480"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":6.8581,"has_fulltext":false,"cited_by_count":113,"citation_normalized_percentile":{"value":0.97027129,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"41","issue":"6","first_page":"2313","last_page":"2332"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9973999857902527,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9968000054359436,"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/superconvergence","display_name":"Superconvergence","score":0.9248994588851929},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7864574193954468},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6418148875236511},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6160627603530884},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.5867878794670105},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5647376179695129},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5572585463523865},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5395867228507996},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.47145137190818787},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.453517347574234},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.4146898090839386},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38868486881256104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30104711651802063},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24523872137069702}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9248994588851929},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7864574193954468},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6418148875236511},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6160627603530884},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.5867878794670105},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5647376179695129},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5572585463523865},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5395867228507996},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.47145137190818787},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.453517347574234},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.4146898090839386},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38868486881256104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30104711651802063},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24523872137069702},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142901398751","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901398751","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W92953806","https://openalex.org/W1595515622","https://openalex.org/W1677560141","https://openalex.org/W1807403118","https://openalex.org/W1963978816","https://openalex.org/W1993788271","https://openalex.org/W1994336408","https://openalex.org/W2010332082","https://openalex.org/W2012229545","https://openalex.org/W2017472233","https://openalex.org/W2018788206","https://openalex.org/W2021411519","https://openalex.org/W2043763125","https://openalex.org/W2050178911","https://openalex.org/W2071036364","https://openalex.org/W2080246801","https://openalex.org/W2087764189","https://openalex.org/W2122602456","https://openalex.org/W2157121531","https://openalex.org/W2165630134","https://openalex.org/W4240023077"],"related_works":["https://openalex.org/W1495993365","https://openalex.org/W1807403118","https://openalex.org/W2087764189","https://openalex.org/W1998702944","https://openalex.org/W1990276724","https://openalex.org/W2740115552","https://openalex.org/W2915376398","https://openalex.org/W976884201","https://openalex.org/W2048132368","https://openalex.org/W582123556"],"abstract_inverted_index":{"In":[0,38],"Part":[1],"I":[2],"of":[3,29,71,82,90,113,134],"this":[4,39],"work":[5],"[SIAM":[6],"J.":[7],"Numer.":[8],"Anal.,":[9],"41":[10],"(2003),":[11],"pp.":[12],"2294--2312],":[13],"we":[14,41,103],"analyzed":[15],"superconvergence":[16,43],"for":[17,44,58,122],"piecewise":[18],"linear":[19],"finite":[20,60],"element":[21,61],"approximations":[22],"on":[23],"triangular":[24],"meshes":[25],"where":[26],"most":[27],"pairs":[28],"triangles":[30],"sharing":[31],"a":[32,53,91,93],"common":[33],"edge":[34],"form":[35,118],"approximate":[36,109],"parallelograms.":[37],"work,":[40],"consider":[42],"general":[45],"unstructured":[46],"but":[47],"shape":[48],"regular":[49],"meshes.":[50],"We":[51,126],"develop":[52],"postprocessing":[54],"gradient":[55,77,81,107],"recovery":[56],"scheme":[57],"the":[59,68,72,80,83,88,105,110,114,132],"solution":[62,85,116],"uh,":[63],"inspired":[64],"in":[65],"part":[66],"by":[67],"smoothing":[69],"iteration":[70],"multigrid":[73],"method.":[74],"This":[75],"recovered":[76],"superconverges":[78],"to":[79,108],"true":[84,115],"and":[86,117],"becomes":[87],"basis":[89],"global":[92],"posteriori":[94],"error":[95,120],"estimate":[96],"that":[97],"is":[98],"often":[99],"asymptotically":[100],"exact.":[101],"Next,":[102],"use":[104],"superconvergent":[106],"Hessian":[111],"matrix":[112],"local":[119],"indicators":[121],"adaptive":[123],"meshing":[124],"algorithms.":[125],"provide":[127],"several":[128],"numerical":[129],"examples":[130],"illustrating":[131],"effectiveness":[133],"our":[135],"procedures.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}