{"id":"https://openalex.org/W3098514373","doi":"https://doi.org/10.1137/19m1271099","title":"Adaptive First-Order System Least-Squares Finite Element Methods for Second-Order Elliptic Equations in Nondivergence Form","display_name":"Adaptive First-Order System Least-Squares Finite Element Methods for Second-Order Elliptic Equations in Nondivergence Form","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3098514373","doi":"https://doi.org/10.1137/19m1271099","mag":"3098514373"},"language":"en","primary_location":{"id":"doi:10.1137/19m1271099","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1271099","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":true,"oa_status":"bronze","oa_url":"https://scholars.cityu.edu.hk/en/publications/adaptive-first-order-system-least-squares-finite-element-methods-","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059376708","display_name":"Weifeng Qiu","orcid":"https://orcid.org/0000-0002-9155-1005"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Weifeng Qiu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100415439","display_name":"Shun Zhang","orcid":"https://orcid.org/0000-0002-5826-8611"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shun Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5059376708"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0783,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.74116922,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"58","issue":"6","first_page":"3286","last_page":"3308"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/finite-element-method","display_name":"Finite element method","score":0.78995680809021},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7874647378921509},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6300309300422668},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5885406732559204},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5839083790779114},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5583691000938416},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.47261857986450195},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.45269495248794556},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.4507637917995453},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4407811760902405},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.4325265884399414},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4293064773082733},{"id":"https://openalex.org/keywords/elliptic-operator","display_name":"Elliptic operator","score":0.4256061911582947},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.41311895847320557}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.78995680809021},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7874647378921509},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6300309300422668},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5885406732559204},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5839083790779114},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5583691000938416},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.47261857986450195},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.45269495248794556},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.4507637917995453},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4407811760902405},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.4325265884399414},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4293064773082733},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.4256061911582947},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.41311895847320557},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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":3,"locations":[{"id":"doi:10.1137/19m1271099","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1271099","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"},{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/adaptive-first-order-system-least-squares-finite-element-methods-","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:pure.atira.dk:publications/9023215d-70ed-4eb0-93be-3f5383964f80","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/9023215d-70ed-4eb0-93be-3f5383964f80","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"QIU, W & ZHANG, S 2020, 'ADAPTIVE FIRST-ORDER SYSTEM LEAST-SQUARES FINITE ELEMENT METHODS FOR SECOND-ORDER ELLIPTIC EQUATIONS IN NONDIVERGENCE FORM', SIAM Journal on Numerical Analysis, vol. 58, no. 6, pp. 3286-3308. https://doi.org/10.1137/19M1271099","raw_type":"article"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/adaptive-first-order-system-least-squares-finite-element-methods-","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1965034652","https://openalex.org/W1972266198","https://openalex.org/W1972877576","https://openalex.org/W1978431441","https://openalex.org/W1992261213","https://openalex.org/W1998803201","https://openalex.org/W2007809587","https://openalex.org/W2008849850","https://openalex.org/W2020552462","https://openalex.org/W2030826026","https://openalex.org/W2041341533","https://openalex.org/W2046300718","https://openalex.org/W2060568111","https://openalex.org/W2068537445","https://openalex.org/W2071942565","https://openalex.org/W2103026454","https://openalex.org/W2132292023","https://openalex.org/W2152917700","https://openalex.org/W2200592550","https://openalex.org/W2223973105","https://openalex.org/W2289792662","https://openalex.org/W2330052780","https://openalex.org/W2552708984","https://openalex.org/W2917203384","https://openalex.org/W2963149381","https://openalex.org/W2963227054","https://openalex.org/W2963671148","https://openalex.org/W2963922304","https://openalex.org/W3016664815","https://openalex.org/W4230108662","https://openalex.org/W4244513512"],"related_works":["https://openalex.org/W4385187474","https://openalex.org/W2519661340","https://openalex.org/W4310279368","https://openalex.org/W2013689478","https://openalex.org/W1897016801","https://openalex.org/W1967896107","https://openalex.org/W1985020803","https://openalex.org/W2054379037","https://openalex.org/W2073319134","https://openalex.org/W2050673833"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"adaptive":[3,68],"first-order":[4,41,81],"system":[5,79],"least-squares":[6,42,95],"finite":[7,23,56,96,102],"element":[8,24,57,97],"methods":[9,25,98],"(LSFEMs)":[10],"for":[11,36,67,163,173,179],"second-order":[12],"elliptic":[13],"partial":[14],"differential":[15],"equations":[16,82],"in":[17,106,160],"nondivergence":[18,38,72],"form.":[19],"Unlike":[20],"the":[21,37,40,85,107,111,118,121,129,133,136,156,164,195,200],"classical":[22],"which":[26,113],"use":[27],"weak":[28,47],"formulations":[29,43],"of":[30,80,94,199],"PDEs":[31],"that":[32,135],"are":[33,104,149,171,191],"not":[34],"applicable":[35],"equation,":[39],"naturally":[44],"have":[45,61],"stable":[46],"forms":[48],"without":[49],"using":[50,99],"integration":[51],"by":[52,83],"parts,":[53],"allow":[54],"simple":[55,100],"approximation":[58],"spaces,":[59],"and":[60,117,144,182,188,197],"built-in":[62],"a":[63,78,88,124,139,142,145],"posteriori":[64,146],"error":[65,147],"estimators":[66],"mesh":[69],"refinements.":[70],"The":[71],"equation":[73],"is":[74,110,120,166],"first":[75],"written":[76],"as":[77,87],"introducing":[84],"gradient":[86],"new":[89],"variable.":[90],"Then,":[91],"two":[92],"versions":[93],"$C^0$":[101],"elements":[103],"developed":[105],"paper.":[108],"One":[109],"$L^2$-LSFEM":[112],"uses":[114],"linear":[115],"elements,":[116],"other":[119],"W-LSFEM":[122,165],"with":[123],"mesh-dependent":[125],"weight":[126],"to":[127,193],"ensure":[128],"optimal":[130],"convergence.":[131],"Under":[132],"assumption":[134,154],"PDE":[137],"has":[138],"unique":[140],"solution,":[141],"priori":[143],"estimates":[148,170],"presented.":[150],"With":[151],"an":[152],"extra":[153],"on":[155,186],"operator":[157],"regularity,":[158],"convergence":[159],"standard":[161],"norms":[162],"also":[167],"discussed.":[168],"$L^2$-error":[169],"derived":[172],"both":[174],"formulations.":[175],"Extensive":[176],"numerical":[177],"experiments":[178],"continuous,":[180],"discontinuous,":[181],"even":[183],"degenerate":[184],"coefficients":[185],"smooth":[187],"singular":[189],"solutions":[190],"performed":[192],"test":[194],"accuracy":[196],"efficiency":[198],"proposed":[201],"methods.":[202]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}