{"id":"https://openalex.org/W2964048411","doi":"https://doi.org/10.1137/16m105513x","title":"A Unified Analysis of Quasi-Optimal Convergence for Adaptive Mixed Finite Element Methods","display_name":"A Unified Analysis of Quasi-Optimal Convergence for Adaptive Mixed Finite Element Methods","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2964048411","doi":"https://doi.org/10.1137/16m105513x","mag":"2964048411"},"language":"en","primary_location":{"id":"doi:10.1137/16m105513x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m105513x","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/A5028500115","display_name":"Jun Hu","orcid":"https://orcid.org/0000-0002-4565-3000"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Hu","raw_affiliation_strings":["LMAM and School of Mathematical Sciences, Peking University, Beijing 100871,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMAM and School of Mathematical Sciences, Peking University, Beijing 100871,China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101766795","display_name":"Guozhu Yu","orcid":"https://orcid.org/0000-0001-6802-420X"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guozhu Yu","raw_affiliation_strings":["School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China","institution_ids":["https://openalex.org/I4800084"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2472,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.76285724,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"56","issue":"1","first_page":"296","last_page":"316"},"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":0.9973000288009644,"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":0.9952999949455261,"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":0.8247565627098083},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7355384826660156},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5525604486465454},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5336547493934631},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5230584740638733},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.499981164932251},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.481838583946228},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4263015389442444},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.4236266016960144},{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"Adaptive mesh refinement","score":0.4224978983402252},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34192126989364624},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15289080142974854}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8247565627098083},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7355384826660156},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5525604486465454},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5336547493934631},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5230584740638733},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.499981164932251},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.481838583946228},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4263015389442444},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4236266016960144},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.4224978983402252},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34192126989364624},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15289080142974854},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m105513x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m105513x","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":[{"id":"https://openalex.org/G2528374576","display_name":null,"funder_award_id":"11401492","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3762157797","display_name":null,"funder_award_id":"91430213","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4448709408","display_name":"\u975e\u7ebf\u6027Kohn-Sham\u65b9\u7a0b\u53ef\u9760\u6027\u9ad8\u7cbe\u5ea6\u6570\u503c\u65b9\u6cd5\u7684\u7814\u7a76","funder_award_id":"11271035","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8051312613","display_name":null,"funder_award_id":"11421101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G873693170","display_name":null,"funder_award_id":"11625101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1574598114","https://openalex.org/W1972200842","https://openalex.org/W1993064848","https://openalex.org/W1995479616","https://openalex.org/W1998674934","https://openalex.org/W2009985306","https://openalex.org/W2011916591","https://openalex.org/W2014744421","https://openalex.org/W2020294233","https://openalex.org/W2023070026","https://openalex.org/W2023930096","https://openalex.org/W2024326406","https://openalex.org/W2026655730","https://openalex.org/W2026991963","https://openalex.org/W2027022149","https://openalex.org/W2029725158","https://openalex.org/W2033698269","https://openalex.org/W2039924562","https://openalex.org/W2043594669","https://openalex.org/W2052476297","https://openalex.org/W2052501455","https://openalex.org/W2059465899","https://openalex.org/W2061326956","https://openalex.org/W2067802257","https://openalex.org/W2072811159","https://openalex.org/W2084743165","https://openalex.org/W2092037996","https://openalex.org/W2094875449","https://openalex.org/W2107813568","https://openalex.org/W2110507293","https://openalex.org/W2118165225","https://openalex.org/W2118551467","https://openalex.org/W2140677965","https://openalex.org/W2156629649","https://openalex.org/W2262198896","https://openalex.org/W2594541596","https://openalex.org/W2911441929","https://openalex.org/W2923738554","https://openalex.org/W2963397795","https://openalex.org/W2996832619","https://openalex.org/W3149667697"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W2059318893","https://openalex.org/W2095582735","https://openalex.org/W4243074410","https://openalex.org/W1965698851"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,139],"present":[4],"a":[5,20,31,65,97,113],"unified":[6],"analysis":[7,63],"of":[8,13,22,52,85,150],"both":[9,70,89,157],"convergence":[10,49],"and":[11,29,50,73,82,93,105,112,147,153,159],"optimality":[12,51],"adaptive":[14,54],"mixed":[15],"finite":[16,26],"element":[17,27],"methods":[18],"for":[19,48,61,88,102,109,144],"class":[21],"problems":[23,155],"when":[24],"the":[25,53,62,86,90,103,110,119,124,128,134,145,151],"spaces":[28],"corresponding":[30],"posteriori":[32],"error":[33],"estimates":[34],"under":[35,56],"consideration":[36],"satisfy":[37],"five":[38,44,142],"hypotheses.":[39],"We":[40],"prove":[41,140],"that":[42],"these":[43,141],"conditions":[45],"are":[46],"sufficient":[47],"algorithms":[55],"consideration.":[57],"The":[58],"main":[59],"ingredient":[60],"is":[64],"new":[66,76],"method":[67,77],"to":[68],"analyze":[69],"discrete":[71,91,99,120,129],"reliability":[72],"quasi-orthogonality.":[74],"This":[75],"arises":[78],"from":[79,118],"an":[80,106],"appropriate":[81],"natural":[83],"choice":[84],"norms":[87],"displacement":[92],"stress":[94,121],"spaces,":[95],"namely,":[96],"mesh-dependent":[98],"$H^1$":[100],"norm":[101,108],"former":[104],"$L^2$":[107],"latter,":[111],"newly":[114],"defined":[115],"projection":[116],"operator":[117],"space":[122,132],"on":[123,133],"coarser":[125],"mesh":[126],"onto":[127],"divergence":[130],"free":[131],"finer":[135],"mesh.":[136],"As":[137],"applications,":[138],"hypotheses":[143],"Raviart--Thomas":[146],"Brezzi--Douglas--Marini":[148],"elements":[149],"Poisson":[152],"Stokes":[154],"in":[156],"two":[158],"three":[160],"dimensions.":[161]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2026-08-08T07:41:36.138363","created_date":"2025-10-10T00:00:00"}