{"id":"https://openalex.org/W1993348678","doi":"https://doi.org/10.1137/120888223","title":"Multiscale Hybrid-Mixed Method","display_name":"Multiscale Hybrid-Mixed Method","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1993348678","doi":"https://doi.org/10.1137/120888223","mag":"1993348678"},"language":"en","primary_location":{"id":"doi:10.1137/120888223","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120888223","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":"green","oa_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3269763","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001469709","display_name":"Rodolfo Araya","orcid":"https://orcid.org/0000-0002-1165-3969"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rodolfo Araya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038482556","display_name":"Christopher Harder","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christopher Harder","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011374809","display_name":"Diego Paredes","orcid":"https://orcid.org/0000-0003-2632-5682"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Diego Paredes","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059362886","display_name":"Fr\u00e9d\u00e9ric Valentin","orcid":"https://orcid.org/0000-0002-5056-7529"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Valentin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.3318,"has_fulltext":false,"cited_by_count":96,"citation_normalized_percentile":{"value":0.96728632,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"51","issue":"6","first_page":"3505","last_page":"3531"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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":0.9998999834060669,"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/T11558","display_name":"Composite Material Mechanics","score":0.998199999332428,"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":0.8669654726982117},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7060073614120483},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6819551587104797},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.66628497838974},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.5938312411308289},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5792156457901001},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5544021129608154},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5509348511695862},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4925266206264496},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4834219217300415},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44926685094833374},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4332221448421478},{"id":"https://openalex.org/keywords/control-variable","display_name":"Control variable","score":0.41291409730911255},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26009994745254517},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2111242711544037},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1386229395866394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8669654726982117},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7060073614120483},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6819551587104797},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.66628497838974},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.5938312411308289},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5792156457901001},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5544021129608154},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5509348511695862},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4925266206264496},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4834219217300415},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44926685094833374},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4332221448421478},{"id":"https://openalex.org/C153240184","wikidata":"https://www.wikidata.org/wiki/Q3243772","display_name":"Control variable","level":2,"score":0.41291409730911255},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26009994745254517},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2111242711544037},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1386229395866394},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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/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/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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/120888223","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120888223","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:americanae.aecid.es:3269763","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3269763","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","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":"Siam Journal On Matrix Analysis And Applications","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:americanae.aecid.es:3334017","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3334017","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","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":"SIAM JOURNAL ON NUMERICAL ANALYSIS","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/135306","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/135306","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"SIAM JOURNAL ON NUMERICAL ANALYSIS","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/148239","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/148239","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"Siam Journal On Matrix Analysis And Applications","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:americanae.aecid.es:3269763","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3269763","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","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":"Siam Journal On Matrix Analysis And Applications","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.6600000262260437}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W136185420","https://openalex.org/W1502992081","https://openalex.org/W1545761024","https://openalex.org/W1601728065","https://openalex.org/W1602383637","https://openalex.org/W1963659668","https://openalex.org/W1967758632","https://openalex.org/W1970446082","https://openalex.org/W1977096265","https://openalex.org/W1994484297","https://openalex.org/W1997640799","https://openalex.org/W2000272165","https://openalex.org/W2005788407","https://openalex.org/W2021411519","https://openalex.org/W2029918260","https://openalex.org/W2052275102","https://openalex.org/W2069555630","https://openalex.org/W2082452417","https://openalex.org/W2129412583","https://openalex.org/W2130350269","https://openalex.org/W2519971170","https://openalex.org/W2923738554"],"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/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W2533824940","https://openalex.org/W2077117602"],"abstract_inverted_index":{"This":[0],"work":[1],"presents":[2],"a":[3,6,11,65,73,89,111,113],"priori":[4],"and":[5,86,117],"posteriori":[7,114],"error":[8,115,123],"analyses":[9],"of":[10,30,40,47,55,59,76,88,101,124],"new":[12],"multiscale":[13],"hybrid-mixed":[14],"method":[15,36,94],"(MHM)":[16],"for":[17,91],"an":[18],"elliptic":[19],"model.":[20],"Specially":[21],"designed":[22],"to":[23],"incorporate":[24],"multiple":[25],"scales":[26],"into":[27],"the":[28,38,41,45,52,56,60,67,77,92,105,122,128,135],"construction":[29],"basis":[31],"functions,":[32],"this":[33],"finite":[34],"element":[35],"relaxes":[37],"continuity":[39,54],"primal":[42,78],"variable":[43],"through":[44],"action":[46],"Lagrange":[48],"multipliers,":[49],"while":[50],"assuring":[51],"strong":[53],"normal":[57],"component":[58],"flux":[61],"(dual":[62],"variable).":[63],"As":[64],"result,":[66],"dual":[68],"variable,":[69,79],"which":[70],"stems":[71],"from":[72],"simple":[74],"postprocessing":[75],"preserves":[80],"local":[81],"conservation.":[82],"We":[83],"prove":[84,118],"existence":[85],"uniqueness":[87],"solution":[90],"MHM":[93],"as":[95,97],"well":[96],"optimal":[98],"convergence":[99],"estimates":[100],"any":[102],"order":[103],"in":[104,127],"natural":[106,129],"norms.":[107,130],"Also,":[108],"we":[109],"propose":[110],"face-residual":[112],"estimator,":[116],"that":[119],"it":[120],"controls":[121],"both":[125],"variables":[126],"Several":[131],"numerical":[132],"tests":[133],"assess":[134],"theoretical":[136],"results.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
