{"id":"https://openalex.org/W4211188765","doi":"https://doi.org/10.3390/e24020255","title":"Recovery-Based Error Estimator for Natural Convection Equations Based on Defect-Correction Methods","display_name":"Recovery-Based Error Estimator for Natural Convection Equations Based on Defect-Correction Methods","publication_year":2022,"publication_date":"2022-02-09","ids":{"openalex":"https://openalex.org/W4211188765","doi":"https://doi.org/10.3390/e24020255","pmid":"https://pubmed.ncbi.nlm.nih.gov/35205549"},"language":"en","primary_location":{"id":"doi:10.3390/e24020255","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020255","pdf_url":"https://www.mdpi.com/1099-4300/24/2/255/pdf?version=1644984728","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/2/255/pdf?version=1644984728","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100421903","display_name":"Lulu Li","orcid":"https://orcid.org/0009-0000-2470-1141"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lulu Li","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103191241","display_name":"Haiyan Su","orcid":"https://orcid.org/0000-0002-0780-3258"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haiyan Su","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028639093","display_name":"Xinlong Feng","orcid":"https://orcid.org/0000-0002-5354-6424"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xinlong Feng","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China","institution_ids":["https://openalex.org/I96908189"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028639093"],"corresponding_institution_ids":["https://openalex.org/I96908189"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.1398,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.31042514,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"24","issue":"2","first_page":"255","last_page":"255"},"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":0.9993000030517578,"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":0.9993000030517578,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/superconvergence","display_name":"Superconvergence","score":0.7646615505218506},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7059780359268188},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6399850249290466},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.6202272176742554},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5468882322311401},{"id":"https://openalex.org/keywords/natural-convection","display_name":"Natural convection","score":0.527951180934906},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4735260009765625},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45802247524261475},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4543444812297821},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.43003982305526733},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4206010103225708},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3965911269187927},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.36181652545928955},{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.3173481822013855},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27658385038375854},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17296847701072693},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.10225757956504822},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08763989806175232},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08107626438140869}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.7646615505218506},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7059780359268188},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6399850249290466},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.6202272176742554},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5468882322311401},{"id":"https://openalex.org/C54791560","wikidata":"https://www.wikidata.org/wiki/Q3285020","display_name":"Natural convection","level":3,"score":0.527951180934906},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4735260009765625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45802247524261475},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4543444812297821},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.43003982305526733},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4206010103225708},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3965911269187927},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.36181652545928955},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.3173481822013855},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27658385038375854},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17296847701072693},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.10225757956504822},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08763989806175232},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08107626438140869},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e24020255","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020255","pdf_url":"https://www.mdpi.com/1099-4300/24/2/255/pdf?version=1644984728","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:35205549","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35205549","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:788c0b18eb9240328fb238106b8e74c3","is_oa":true,"landing_page_url":"https://doaj.org/article/788c0b18eb9240328fb238106b8e74c3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 24, Iss 2, p 255 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/2/255/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24020255","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 24; Issue 2; Pages: 255","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8871441","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8871441","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e24020255","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020255","pdf_url":"https://www.mdpi.com/1099-4300/24/2/255/pdf?version=1644984728","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4211188765.pdf"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W219908362","https://openalex.org/W623510916","https://openalex.org/W1979389543","https://openalex.org/W1986320166","https://openalex.org/W1988552931","https://openalex.org/W1989594010","https://openalex.org/W1995404822","https://openalex.org/W2014289408","https://openalex.org/W2029604506","https://openalex.org/W2031440284","https://openalex.org/W2041179520","https://openalex.org/W2047518170","https://openalex.org/W2062398006","https://openalex.org/W2111352333","https://openalex.org/W2136719269","https://openalex.org/W2142484159","https://openalex.org/W2164470476","https://openalex.org/W2239389536","https://openalex.org/W2419322245","https://openalex.org/W2466566907","https://openalex.org/W2547081703","https://openalex.org/W2560636309","https://openalex.org/W2594247582","https://openalex.org/W2599417779","https://openalex.org/W2779759640","https://openalex.org/W2781635282","https://openalex.org/W2794122374","https://openalex.org/W2898344165","https://openalex.org/W2910609445","https://openalex.org/W3031404688","https://openalex.org/W3035181138","https://openalex.org/W3038790778","https://openalex.org/W3082563703","https://openalex.org/W3112952487","https://openalex.org/W3123165850","https://openalex.org/W3144682514","https://openalex.org/W3157316160","https://openalex.org/W3183284562","https://openalex.org/W3213573088","https://openalex.org/W6792777625","https://openalex.org/W6794643805"],"related_works":["https://openalex.org/W2094577950","https://openalex.org/W2031157121","https://openalex.org/W1565666028","https://openalex.org/W2891538916","https://openalex.org/W2160252404","https://openalex.org/W4230524683","https://openalex.org/W3141012097","https://openalex.org/W185121461","https://openalex.org/W1968948586","https://openalex.org/W3045891854"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,53],"propose":[4],"an":[5],"adaptive":[6],"defect-correction":[7,15],"method":[8,16,98],"for":[9,20],"natural":[10],"convection":[11,27],"(NC)":[12],"equations.":[13],"A":[14],"(DCM)":[17],"is":[18],"proposed":[19,97],"solving":[21],"NC":[22],"equations":[23],"to":[24],"overcome":[25],"the":[26,38,44,47,50,63,77,85,90,96],"dominance":[28],"problem":[29],"caused":[30],"by":[31,84,101],"a":[32,55],"high":[33],"Rayleigh":[34],"number.":[35],"To":[36],"solve":[37],"large":[39],"amount":[40],"of":[41,46,49,62,95],"computation":[42],"and":[43,66,72,93],"discontinuity":[45],"gradient":[48,64],"numerical":[51,103],"solution,":[52],"combine":[54],"new":[56],"recovery-type":[57],"posteriori":[58],"estimator":[59],"in":[60],"view":[61],"recovery":[65],"superconvergent":[67],"theory.":[68],"The":[69],"presented":[70],"reliability":[71],"efficiency":[73,94],"analysis":[74],"shows":[75],"that":[76],"true":[78],"error":[79,87],"can":[80],"be":[81],"effectively":[82],"bounded":[83],"recovery-based":[86],"estimator.":[88],"Finally,":[89],"stability,":[91],"accuracy":[92],"are":[99],"confirmed":[100],"several":[102],"investigations.":[104]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
