{"id":"https://openalex.org/W1998985645","doi":"https://doi.org/10.1137/130941742","title":"Analysis of an Adaptive Finite Element Method for Recovering the Robin Coefficient","display_name":"Analysis of an Adaptive Finite Element Method for Recovering the Robin Coefficient","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1998985645","doi":"https://doi.org/10.1137/130941742","mag":"1998985645"},"language":"en","primary_location":{"id":"doi:10.1137/130941742","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130941742","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5048462943","display_name":"Yifeng Xu","orcid":"https://orcid.org/0009-0006-3216-1310"},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yifeng Xu","raw_affiliation_strings":["Shanghai Normal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Normal University","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090609331","display_name":"Jun Zou","orcid":"https://orcid.org/0000-0002-4809-7724"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jun Zou","raw_affiliation_strings":["Department of Mathematics, The Chinese University of Hong Kong, Shatin, N"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Shatin, N","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.499,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.86812933,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"53","issue":"2","first_page":"622","last_page":"644"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9988999962806702,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9909999966621399,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8107277154922485},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6849730014801025},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.6118628978729248},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5651178359985352},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5628052353858948},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5360308885574341},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4786361753940582},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.47272437810897827},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4609999656677246},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4418609142303467},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16184115409851074},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12210896611213684}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8107277154922485},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6849730014801025},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.6118628978729248},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5651178359985352},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5628052353858948},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5360308885574341},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4786361753940582},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.47272437810897827},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4609999656677246},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4418609142303467},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16184115409851074},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12210896611213684},{"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},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/130941742","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130941742","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.704.1941","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.704.1941","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cuhk.edu.hk/%7Ezou/publication/sicon14xu.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.699999988079071}],"awards":[{"id":"https://openalex.org/G3054894371","display_name":null,"funder_award_id":"E03004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G577525076","display_name":null,"funder_award_id":"11201307","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7596950192","display_name":null,"funder_award_id":"E03004","funder_id":"https://openalex.org/F4320321881","funder_display_name":"Shanghai Municipal Education Commission"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321881","display_name":"Shanghai Municipal Education Commission","ror":"https://ror.org/05tewj457"},{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"},{"id":"https://openalex.org/F4320336024","display_name":"Specialized Research Fund for the Doctoral Program of Higher Education of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W184188664","https://openalex.org/W1543766063","https://openalex.org/W1593038947","https://openalex.org/W1963490038","https://openalex.org/W1964524533","https://openalex.org/W1968015765","https://openalex.org/W1976173851","https://openalex.org/W1978687734","https://openalex.org/W1995404822","https://openalex.org/W1997468635","https://openalex.org/W1997471340","https://openalex.org/W2001617395","https://openalex.org/W2002604046","https://openalex.org/W2007239852","https://openalex.org/W2009985306","https://openalex.org/W2014303698","https://openalex.org/W2026617830","https://openalex.org/W2026703029","https://openalex.org/W2027521015","https://openalex.org/W2036444686","https://openalex.org/W2044333097","https://openalex.org/W2044959876","https://openalex.org/W2046126451","https://openalex.org/W2057393095","https://openalex.org/W2063085789","https://openalex.org/W2072811159","https://openalex.org/W2081585768","https://openalex.org/W2084132784","https://openalex.org/W2084743165","https://openalex.org/W2084780726","https://openalex.org/W2093581986","https://openalex.org/W2097879622","https://openalex.org/W2100950337","https://openalex.org/W2103047177","https://openalex.org/W2107813568","https://openalex.org/W2111838745","https://openalex.org/W2128722493","https://openalex.org/W2153808555","https://openalex.org/W2169143985","https://openalex.org/W2179536916","https://openalex.org/W2219314431","https://openalex.org/W2324833387","https://openalex.org/W2328632875","https://openalex.org/W2496227181","https://openalex.org/W2962932345","https://openalex.org/W2964192538","https://openalex.org/W4252335891"],"related_works":["https://openalex.org/W3016180395","https://openalex.org/W2337734184","https://openalex.org/W2388364587","https://openalex.org/W2322955667","https://openalex.org/W2373176546","https://openalex.org/W2127000180","https://openalex.org/W2050033254","https://openalex.org/W2561531189","https://openalex.org/W2152224705","https://openalex.org/W2374214022"],"abstract_inverted_index":{"Based":[0],"on":[1],"a":[2,4,22,30,49,61,80],"new":[3],"posteriori":[5,31,50,62],"error":[6,32,51,63],"estimator,":[7],"an":[8,87],"adaptive":[9,71,77],"finite":[10],"element":[11],"method":[12],"is":[13],"proposed":[14],"for":[15,37,46,53,113],"recovering":[16],"the":[17,47,60,70,76,103,107,114,126,129],"Robin":[18,95],"coefficient":[19],"involved":[20],"in":[21,86],"diffusion":[23],"system":[24,105],"from":[25,65],"some":[26,91],"boundary":[27],"measurement.":[28],"The":[29],"estimator":[33,64],"cannot":[34],"be":[35],"derived":[36],"this":[38],"ill-posed":[39],"nonlinear":[40],"inverse":[41,116],"problem":[42],"as":[43],"was":[44],"done":[45],"existing":[48],"estimators":[52],"direct":[54],"problems.":[55],"Instead,":[56],"we":[57],"shall":[58],"derive":[59],"our":[66],"convergence":[67],"analysis":[68],"of":[69,83,106,128],"algorithm.":[72,130],"We":[73],"prove":[74],"that":[75],"algorithm":[78],"guarantees":[79],"convergent":[81],"subsequence":[82],"discrete":[84],"solutions":[85],"energy":[88],"norm":[89],"to":[90,124],"exact":[92],"triplet":[93],"(the":[94],"coefficient,":[96],"state":[97],"and":[98],"costate":[99],"variables)":[100],"determined":[101],"by":[102],"optimality":[104],"least-squares":[108],"formulation":[109],"with":[110],"Tikhonov":[111],"regularization":[112],"concerned":[115],"problem.":[117],"Some":[118],"numerical":[119],"results":[120],"are":[121],"also":[122],"reported":[123],"illustrate":[125],"performance":[127]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
