{"id":"https://openalex.org/W1997640799","doi":"https://doi.org/10.1137/s0036142902406636","title":"Analysis of a Two-Scale, Locally Conservative Subgrid Upscaling for Elliptic Problems","display_name":"Analysis of a Two-Scale, Locally Conservative Subgrid Upscaling for Elliptic Problems","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1997640799","doi":"https://doi.org/10.1137/s0036142902406636","mag":"1997640799"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142902406636","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902406636","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"],"raw_orcid":null,"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"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034967156"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":7.2551,"has_fulltext":false,"cited_by_count":145,"citation_normalized_percentile":{"value":0.97385751,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"42","issue":"2","first_page":"576","last_page":"598"},"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":0.9980000257492065,"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/nabla-symbol","display_name":"Nabla symbol","score":0.7808400988578796},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7256313562393188},{"id":"https://openalex.org/keywords/elliptic-operator","display_name":"Elliptic operator","score":0.5338941812515259},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.4735618829727173},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46193018555641174},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44348204135894775},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.4198925495147705},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41052526235580444},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3836158215999603},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3273700475692749},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25397592782974243},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.22990408539772034},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08111372590065002}],"concepts":[{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.7808400988578796},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7256313562393188},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.5338941812515259},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.4735618829727173},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46193018555641174},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44348204135894775},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.4198925495147705},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41052526235580444},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3836158215999603},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3273700475692749},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25397592782974243},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.22990408539772034},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08111372590065002},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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":2,"locations":[{"id":"doi:10.1137/s0036142902406636","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902406636","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:10.1.1.574.207","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.574.207","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_2004.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.6399999856948853,"display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G2037010823","display_name":"KDI: Multiscale Physics-Based Simulation of Fluid Flow for  Energy and Environmental Applications","funder_award_id":"9873326","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2292737138","display_name":"A Posteriori Error Estimation and Up-Scaling for Mixed      Finite Element Methods","funder_award_id":"9707015","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":29,"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/W1866311589","https://openalex.org/W1974462837","https://openalex.org/W1980455776","https://openalex.org/W2029918260","https://openalex.org/W2032730144","https://openalex.org/W2040933131","https://openalex.org/W2041523977","https://openalex.org/W2051682834","https://openalex.org/W2061172735","https://openalex.org/W2062002217","https://openalex.org/W2062618977","https://openalex.org/W2070033465","https://openalex.org/W2078045751","https://openalex.org/W2079816657","https://openalex.org/W2080474884","https://openalex.org/W2097842356","https://openalex.org/W2099936591","https://openalex.org/W2116756031","https://openalex.org/W2206315619","https://openalex.org/W2464997744","https://openalex.org/W3038830718","https://openalex.org/W3149667697","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W2229925025","https://openalex.org/W1539596337","https://openalex.org/W33469805","https://openalex.org/W1855007440","https://openalex.org/W2788247819","https://openalex.org/W2914699178","https://openalex.org/W4301243416","https://openalex.org/W2024985363","https://openalex.org/W2156911440","https://openalex.org/W3102850576"],"abstract_inverted_index":{"We":[0,49,68,138],"present":[1],"a":[2,11,24,31,46,86,155,211,218],"two-scale":[3,196,248],"theoretical":[4],"framework":[5],"for":[6,246],"approximating":[7],"the":[8,51,78,127,135,142,184,187,231,234,247],"solution":[9],"of":[10,90,213],"second":[12],"order":[13,256],"elliptic":[14,17,52],"problem.":[15,189],"The":[16,151],"coefficient":[18],"is":[19,82,131,170,176,204,227,244],"assumed":[20],"to":[21,84,163,178,182,229,233,238,253],"vary":[22],"on":[23,30,37,45,73],"scale":[25,71,149],"that":[26,41,111,180],"can":[27,207],"be":[28,43,208],"resolved":[29],"fine":[32],"numerical":[33,223],"grid,":[34],"but":[35],"limits":[36],"computational":[38],"power":[39],"require":[40],"computations":[42],"performed":[44],"coarse":[47,79,96,136,146],"grid.":[48,80],"consider":[50],"problem":[53,144,153],"in":[54,172],"mixed":[55,192,197,202,241],"variational":[56,143,214],"form":[57],"over":[58,77,134],"$W":[59,91],"\\times":[60,65,92,101,107,160,166],"{\\bf":[61,93,102,115,161],"V}":[62,121],"\\subset":[63],"L^2":[64],"H({\\rm":[66],"div})$.":[67],"base":[69],"our":[70],"expansion":[72],"local":[74],"mass":[75],"conservation":[76],"It":[81],"used":[83,177,228,252],"define":[85],"direct":[87],"sum":[88],"decomposition":[89],"V}$":[94,109,130],"into":[95,145],"and":[97,104,117,125,147,174,251],"\"subgrid\"":[98],"subspaces":[99],"$W_c":[100,159],"V}_c$":[103,162],"$\\delta":[105,164],"W":[106,165],"\\delta{\\bf":[108,120,167],"such":[110],"(1)":[112],"$\\nabla":[113,118],"\\cdot":[114,119],"V}_c=W_c$":[116],"=":[122],"\\delta":[123],"W$,":[124],"(2)":[126],"space":[128],"$\\delta{\\bf":[129],"locally":[132],"supported":[133],"mesh.":[137],"then":[139],"explicitly":[140],"decompose":[141],"subgrid":[148,152,185,235],"problems.":[150],"gives":[154],"well-defined":[156],"operator":[157,236],"taking":[158],"V}$,":[168],"which":[169,206],"localized":[171],"space,":[173],"it":[175],"upscale,":[179],"is,":[181],"remove":[183],"from":[186],"coarse-scale":[188],"Using":[190],"standard":[191],"finite":[193],"element":[194],"spaces,":[195],"spaces":[198,250],"are":[199],"defined.":[200],"A":[201,222,240],"approximation":[203,232,249],"defined,":[205],"viewed":[209],"as":[210],"type":[212],"multiscale":[215],"method":[216,242],"or":[217],"residual-free":[219],"bubble":[220],"technique.":[221],"Green's":[224],"function":[225],"approach":[226],"make":[230],"efficient":[237],"compute.":[239],"$\\pi$-operator":[243],"defined":[245],"show":[254],"optimal":[255],"error":[257],"estimates.":[258]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":5}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}
