{"id":"https://openalex.org/W2064862875","doi":"https://doi.org/10.1137/100815918","title":"Corrector Theory for MsFEM and HMM in Random Media","display_name":"Corrector Theory for MsFEM and HMM in Random Media","publication_year":2011,"publication_date":"2011-10-01","ids":{"openalex":"https://openalex.org/W2064862875","doi":"https://doi.org/10.1137/100815918","mag":"2064862875"},"language":"en","primary_location":{"id":"doi:10.1137/100815918","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100815918","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1011.5194","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047341994","display_name":"Guillaume Bal","orcid":"https://orcid.org/0000-0002-4792-7546"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Guillaume Bal","raw_affiliation_strings":["Columbia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Columbia University","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084054664","display_name":"Wenjia Jing","orcid":"https://orcid.org/0000-0001-8860-6880"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wenjia Jing","raw_affiliation_strings":["Columbia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Columbia University","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047341994"],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":null,"apc_paid":null,"fwci":3.9132,"has_fulltext":true,"cited_by_count":54,"citation_normalized_percentile":{"value":0.93763732,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"9","issue":"4","first_page":"1549","last_page":"1587"},"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/T11558","display_name":"Composite Material Mechanics","score":0.9994999766349792,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.8274948596954346},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6628397107124329},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5953590869903564},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.5722842216491699},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5077846646308899},{"id":"https://openalex.org/keywords/random-field","display_name":"Random field","score":0.488505482673645},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.45514020323753357},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4523351192474365},{"id":"https://openalex.org/keywords/gaussian-random-field","display_name":"Gaussian random field","score":0.4451358914375305},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4427233338356018},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42518073320388794},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.3923836648464203},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36138811707496643},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34145471453666687},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.340417742729187},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27731794118881226},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20640137791633606},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12074252963066101}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.8274948596954346},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6628397107124329},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5953590869903564},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.5722842216491699},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5077846646308899},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.488505482673645},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.45514020323753357},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4523351192474365},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.4451358914375305},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4427233338356018},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42518073320388794},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.3923836648464203},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36138811707496643},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34145471453666687},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.340417742729187},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27731794118881226},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20640137791633606},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12074252963066101},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100815918","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100815918","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1011.5194","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1011.5194","pdf_url":"https://arxiv.org/pdf/1011.5194","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1011.5194","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1011.5194","pdf_url":"https://arxiv.org/pdf/1011.5194","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1130514660","display_name":null,"funder_award_id":"DMS-0804696","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1620224260","display_name":"Partial Differential Equations with random coefficients and Inverse Problems","funder_award_id":"0804696","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1390923","https://openalex.org/W137685157","https://openalex.org/W960591838","https://openalex.org/W1543119018","https://openalex.org/W1580561995","https://openalex.org/W1592958377","https://openalex.org/W1966480196","https://openalex.org/W1967011851","https://openalex.org/W1974309308","https://openalex.org/W1997640799","https://openalex.org/W2003490810","https://openalex.org/W2029918260","https://openalex.org/W2038330765","https://openalex.org/W2076488661","https://openalex.org/W2117440981","https://openalex.org/W2117601947","https://openalex.org/W2802739963","https://openalex.org/W2962804622","https://openalex.org/W2964230546","https://openalex.org/W3021722416","https://openalex.org/W3214098784"],"related_works":["https://openalex.org/W3101730079","https://openalex.org/W4285599464","https://openalex.org/W2262012800","https://openalex.org/W3083204305","https://openalex.org/W2090206927","https://openalex.org/W2013997342","https://openalex.org/W3008047311","https://openalex.org/W2112359133","https://openalex.org/W31626890","https://openalex.org/W4287599036"],"abstract_inverted_index":{"We":[0,76,95,143,274],"analyze":[1],"the":[2,11,18,47,51,65,69,72,78,82,87,101,105,124,130,139,146,158,161,165,175,179,185,197,200,207,211,223,239,249,259,286],"random":[3,54,66,90,108,162,180,240,287],"fluctuations":[4,67,91,125,163,181,241,260,288],"of":[5,68,81,89,107,132,148,160,164,199,213,234],"several":[6],"multiscale":[7,12,22,39,102,176,201],"algorithms,":[8],"such":[9,149,169],"as":[10,138,152,191],"finite":[13,19],"element":[14,20],"method":[15,23,254],"(MsFEM)":[16],"and":[17,58,112,153,183,229,245,264],"heterogeneous":[21,36],"(HMM),":[24],"that":[25,123,174,222,284],"have":[26],"been":[27],"developed":[28],"to":[29,44,135,195],"solve":[30],"partial":[31],"differential":[32],"equations":[33],"with":[34,64,110,157,231,256,271,279],"highly":[35,52],"coefficients.":[37],"Such":[38],"algorithms":[40,103],"are":[41,215],"often":[42],"shown":[43],"correctly":[45,237,257],"capture":[46,238],"homogenization":[48,74,214],"limit":[49,147,156],"when":[50],"oscillatory":[53],"medium":[55],"is":[56,62,92,221],"stationary":[57],"ergodic.":[59],"This":[60,188],"paper":[61],"concerned":[63],"solution":[70],"about":[71],"deterministic":[73],"limit.":[75],"consider":[77],"simplified":[79],"setting":[80],"one-dimensional":[83],"elliptic":[84],"equation,":[85],"where":[86,206],"theory":[88,99,212],"well":[93],"understood.":[94],"develop":[96],"a":[97,116,232,276],"fluctuation":[98],"for":[100,210,243,261],"in":[104,127,129,203,248,269,289],"presence":[106],"environments":[109],"short-range":[111,244,272],"long-range":[113,246,262],"correlations.":[114],"For":[115],"given":[117],"mesh":[118],"size":[119,268],",":[120,236],"we":[121,172,219],"show":[122],"converge":[126],"distribution":[128,159],"space":[131],"continuous":[133,166],"paths":[134],"Gaussian":[136,150],"processes":[137,151],"correlation":[140],"length":[141],".":[142],"next":[144],"derive":[145],"compare":[154],"this":[155],"model.":[167],"When":[168],"limits":[170],"agree,":[171],"conclude":[173],"algorithm":[177,202],"captures":[178,258,285],"accurately":[182],"passes":[184],"corrector":[186],"test.":[187],"property":[189],"serves":[190],"an":[192,280],"interesting":[193],"benchmark":[194],"assess":[196],"behavior":[198],"practical":[204],"situations":[205],"assumptions":[208],"necessary":[209],"not":[216],"met.":[217],"What":[218],"find":[220],"computationally":[224],"more":[225],"expensive":[226,253],"methods":[227],"MsFEM,":[228],"HMM":[230,255],"choice":[233],"parameter":[235],"both":[242],"oscillations":[247,263],"medium.":[250],"The":[251],"less":[252],"strongly":[265],"amplifies":[266],"their":[267],"media":[270],"oscillations.":[273],"present":[275],"modified":[277],"scheme":[278],"intermediate":[281],"computational":[282],"cost":[283],"all":[290],"cases.":[291]},"counts_by_year":[{"year":2019,"cited_by_count":33},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}
