{"id":"https://openalex.org/W3119551664","doi":"https://doi.org/10.1137/20m134383x","title":"Error Analysis of Finite Element Approximations of Diffusion Coefficient Identification for Elliptic and Parabolic Problems","display_name":"Error Analysis of Finite Element Approximations of Diffusion Coefficient Identification for Elliptic and Parabolic Problems","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3119551664","doi":"https://doi.org/10.1137/20m134383x","mag":"3119551664"},"language":"en","primary_location":{"id":"doi:10.1137/20m134383x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m134383x","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/A5039605463","display_name":"Bangti Jin","orcid":"https://orcid.org/0000-0002-3775-9155"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]},{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB","HK"],"is_corresponding":true,"raw_author_name":"Bangti Jin","raw_affiliation_strings":["\\ddagger Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong","\\dagger Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK"],"affiliations":[{"raw_affiliation_string":"\\ddagger Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"\\dagger Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002445122","display_name":"Zhi Zhou","orcid":"https://orcid.org/0000-0002-3439-0313"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]},{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB","HK"],"is_corresponding":false,"raw_author_name":"Zhi Zhou","raw_affiliation_strings":["\\dagger Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK","\\ddagger Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong"],"affiliations":[{"raw_affiliation_string":"\\dagger Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK","institution_ids":["https://openalex.org/I45129253"]},{"raw_affiliation_string":"\\ddagger Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039605463"],"corresponding_institution_ids":["https://openalex.org/I14243506","https://openalex.org/I45129253"],"apc_list":null,"apc_paid":null,"fwci":6.8432,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.97982002,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"1","first_page":"119","last_page":"142"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991999864578247,"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":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8436622619628906},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6589455604553223},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6024741530418396},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.592998743057251},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.541720449924469},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5187849998474121},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.49380549788475037},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.48503369092941284},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4162937104701996},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39025411009788513},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2826523184776306}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8436622619628906},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6589455604553223},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6024741530418396},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.592998743057251},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.541720449924469},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5187849998474121},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.49380549788475037},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.48503369092941284},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4162937104701996},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39025411009788513},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2826523184776306},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/20m134383x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m134383x","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"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/93877","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/93877","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2343787110","display_name":"Stochastic iterative regularization: theory, algorithms and applications","funder_award_id":"EP/T000864/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2543385244","display_name":null,"funder_award_id":"EP/T000864/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1970958776","https://openalex.org/W1982386299","https://openalex.org/W1984583900","https://openalex.org/W1993491255","https://openalex.org/W2022816471","https://openalex.org/W2023682725","https://openalex.org/W2024488576","https://openalex.org/W2034187542","https://openalex.org/W2045623154","https://openalex.org/W2053695265","https://openalex.org/W2054860673","https://openalex.org/W2068415618","https://openalex.org/W2068561518","https://openalex.org/W2069920132","https://openalex.org/W2070923502","https://openalex.org/W2078860422","https://openalex.org/W2093791065","https://openalex.org/W2109806713","https://openalex.org/W2163824141","https://openalex.org/W2471307131","https://openalex.org/W2521274054","https://openalex.org/W2619423951","https://openalex.org/W2770598244","https://openalex.org/W2883121725","https://openalex.org/W2962904825","https://openalex.org/W2963221114","https://openalex.org/W2963974297","https://openalex.org/W3098166756"],"related_works":["https://openalex.org/W4297070182","https://openalex.org/W4287752683","https://openalex.org/W3206471890","https://openalex.org/W2085547843","https://openalex.org/W2028586620","https://openalex.org/W3000396883","https://openalex.org/W4288329226","https://openalex.org/W2046313492","https://openalex.org/W2755429276","https://openalex.org/W2089181747"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3],"present":[4],"a":[5,11,68,100],"novel":[6],"error":[7,97,118],"analysis":[8],"for":[9,52,83,107],"recovering":[10],"spatially":[12],"dependent":[13],"diffusion":[14],"coefficient":[15,56],"in":[16,60,62],"an":[17,33],"elliptic":[18,85],"or":[19],"parabolic":[20,64,87],"problem.":[21],"It":[22],"is":[23],"based":[24],"on":[25,78],"the":[26,41,63,74,79,117],"standard":[27,95],"regularized":[28],"output":[29],"least-squares":[30],"formulation":[31],"with":[32,46],"$H^1(\\Omega)$":[34],"seminorm":[35],"penalty":[36],"and":[37,55,57,86],"then":[38],"discretized":[39],"using":[40],"Galerkin":[42],"finite":[43,50],"element":[44],"method":[45],"conforming":[47],"piecewise":[48],"linear":[49],"elements":[51],"both":[53,84],"state":[54],"backward":[58],"Euler":[59],"time":[61],"case.":[65],"We":[66],"derive":[67],"priori":[69],"weighted":[70],"$L^2(\\Omega)$":[71,96],"estimates":[72,91,98],"where":[73],"constants":[75],"depend":[76],"only":[77],"given":[80],"problem":[81,109],"data":[82],"cases.":[88],"Further,":[89],"these":[90],"also":[92],"allow":[93],"deriving":[94],"under":[99],"positivity":[101],"condition":[102],"that":[103],"can":[104],"be":[105],"verified":[106],"certain":[108],"data.":[110],"Numerical":[111],"experiments":[112],"are":[113],"provided":[114],"to":[115],"complement":[116],"analysis.":[119]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}