{"id":"https://openalex.org/W1966922361","doi":"https://doi.org/10.1137/050631811","title":"Subgrid Upscaling and Mixed Multiscale Finite Elements","display_name":"Subgrid Upscaling and Mixed Multiscale Finite Elements","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1966922361","doi":"https://doi.org/10.1137/050631811","mag":"1966922361"},"language":"en","primary_location":{"id":"doi:10.1137/050631811","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050631811","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/A5034967156","display_name":"Todd Arbogast","orcid":"https://orcid.org/0000-0001-9692-5478"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Todd Arbogast","raw_affiliation_strings":["Department of Mathematics, University of Texas, 1 University Station C1200, Austin, TX 78712, and Institute for Computational Engineering and Sciences,","University of Texas, 1 University Station C0200, Austin, TX 78712"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Texas, 1 University Station C1200, Austin, TX 78712, and Institute for Computational Engineering and Sciences,","institution_ids":[]},{"raw_affiliation_string":"University of Texas, 1 University Station C0200, Austin, TX 78712","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011749423","display_name":"Kirsten J. Boyd","orcid":null},"institutions":[{"id":"https://openalex.org/I167672050","display_name":"Eureka College","ror":"https://ror.org/04ybtcs72","country_code":"US","type":"education","lineage":["https://openalex.org/I167672050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kirsten J. Boyd","raw_affiliation_strings":["Eureka College"],"affiliations":[{"raw_affiliation_string":"Eureka College","institution_ids":["https://openalex.org/I167672050"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034967156"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":5.0538,"has_fulltext":false,"cited_by_count":133,"citation_normalized_percentile":{"value":0.95454746,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"44","issue":"3","first_page":"1150","last_page":"1171"},"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":0.9998000264167786,"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":0.9995999932289124,"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/superconvergence","display_name":"Superconvergence","score":0.8227974772453308},{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.8205217123031616},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8058823347091675},{"id":"https://openalex.org/keywords/oversampling","display_name":"Oversampling","score":0.7320678234100342},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5712413787841797},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5264062285423279},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.4633086025714874},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4504099190235138},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43055883049964905},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11216893792152405}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.8227974772453308},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.8205217123031616},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8058823347091675},{"id":"https://openalex.org/C197323446","wikidata":"https://www.wikidata.org/wiki/Q331222","display_name":"Oversampling","level":3,"score":0.7320678234100342},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5712413787841797},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5264062285423279},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.4633086025714874},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4504099190235138},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43055883049964905},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11216893792152405},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C49040817","wikidata":"https://www.wikidata.org/wiki/Q193091","display_name":"Optoelectronics","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C46362747","wikidata":"https://www.wikidata.org/wiki/Q173431","display_name":"CMOS","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050631811","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050631811","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:CiteSeerX.psu:10.1.1.551.6865","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.551.6865","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://users.ices.utexas.edu/~arbogast/PaperArchive/Arbogast_Boyd_2006.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7823554765","display_name":"Development and Application of Subgrid Upscaling","funder_award_id":"0408489","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W136185420","https://openalex.org/W190146808","https://openalex.org/W1492326914","https://openalex.org/W1586623601","https://openalex.org/W1637323070","https://openalex.org/W1708679080","https://openalex.org/W1785220882","https://openalex.org/W1852082788","https://openalex.org/W1966480196","https://openalex.org/W1974309308","https://openalex.org/W1974462837","https://openalex.org/W1997640799","https://openalex.org/W2005788407","https://openalex.org/W2014983931","https://openalex.org/W2024798661","https://openalex.org/W2029918260","https://openalex.org/W2034532318","https://openalex.org/W2038330765","https://openalex.org/W2040933131","https://openalex.org/W2051682834","https://openalex.org/W2061172735","https://openalex.org/W2062002217","https://openalex.org/W2070033465","https://openalex.org/W2078045751","https://openalex.org/W2157721313","https://openalex.org/W3149667697","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W2094577950","https://openalex.org/W2031157121","https://openalex.org/W2891538916","https://openalex.org/W1565666028","https://openalex.org/W2766503024","https://openalex.org/W4230524683","https://openalex.org/W2160252404","https://openalex.org/W3141012097","https://openalex.org/W1968948586","https://openalex.org/W2042970891"],"abstract_inverted_index":{"Second":[0],"order":[1,12,78,133],"elliptic":[2],"problems":[3],"in":[4,90],"divergence":[5],"form":[6],"with":[7],"a":[8,99,169],"highly":[9],"varying":[10],"leading":[11],"coefficient":[13],"on":[14,21,104,147],"the":[15,56,68,76,91,96,108,116,131,148,173],"scale":[16,88],"epsilon":[17,28],"can":[18,44],"be":[19,45,65],"approximated":[20],"coarse":[22],"meshes":[23],"of":[24,55,107,153,159],"spacing":[25],"H":[26],"\\gg":[27],"only":[29,146],"if":[30,128],"one":[31,74,129],"uses":[32,75,130],"special":[33],"techniques.":[34],"The":[35,60,141],"mixed":[36],"variational":[37],"multiscale":[38,69,100],"method,":[39],"also":[40],"called":[41],"subgrid":[42,58,111],"upscaling,":[43],"used,":[46,168],"and":[47,81,138,155],"this":[48],"method":[49,61,72,113],"is":[50,62,118,157,166,176],"extended":[51],"to":[52,64,67],"allow":[53],"oversampling":[54,165],"local":[57],"problems.":[59],"shown":[63],"equivalent":[66],"finite":[70],"element":[71],"when":[73,162],"lowest":[77],"Raviart--Thomas":[79],"spaces":[80,137],"provided":[82],"that":[83,115],"there":[84],"are":[85],"no":[86,139],"fine":[87],"components":[89],"source":[92],"function":[93],"f.":[94],"In":[95],"periodic":[97],"setting,":[98],"error":[101,117,142],"analysis":[102],"based":[103],"homogenization":[105],"theory":[106],"more":[109],"general":[110],"upscaling":[112],"shows":[114],"O(epsilon+Hm":[119],"+":[120],"\\sqrt":[121],"epsilon/H":[122],"),":[123],"where":[124],"m=1.":[125,163],"Moreover,":[126],"m=2":[127],"second":[132],"Brezzi-Douglas-Marini":[134],"or":[135],"Brezzi-Douglas-Dur\u00e1n-Fortin":[136],"oversampling.":[140],"bounding":[143],"constant":[144],"depends":[145],"Hm":[149],"-":[150],"1":[151],"-norm":[152],"f":[154],"so":[156],"independent":[158],"small":[160],"scales":[161],"When":[164],"not":[167],"superconvergence":[170],"result":[171],"for":[172],"pressure":[174],"approximation":[175],"shown.":[177]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":38},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
