{"id":"https://openalex.org/W2076488661","doi":"https://doi.org/10.1137/060654207","title":"Analysis of the Multiscale Finite Element Method for Nonlinear and Random Homogenization Problems","display_name":"Analysis of the Multiscale Finite Element Method for Nonlinear and Random Homogenization Problems","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2076488661","doi":"https://doi.org/10.1137/060654207","mag":"2076488661"},"language":"en","primary_location":{"id":"doi:10.1137/060654207","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060654207","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/A5086480330","display_name":"Zhangxin Chen","orcid":"https://orcid.org/0000-0002-9107-1925"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhangxin Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065295336","display_name":"Tatyana Y. Savchuk","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tatyana Y. Savchuk","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086480330"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8811,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.90719946,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"46","issue":"1","first_page":"260","last_page":"279"},"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":0.9998000264167786,"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":0.9995999932289124,"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":0.9723963737487793},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7425480484962463},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7378167510032654},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6757363677024841},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5548158288002014},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4117036759853363},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05551978945732117}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.9723963737487793},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7425480484962463},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7378167510032654},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6757363677024841},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5548158288002014},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4117036759853363},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05551978945732117},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/060654207","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060654207","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:bibcyt.ucla.edu.ve:T070300015738/13","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300015738/13&Nombrebd=Bciucla","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1543119018","https://openalex.org/W1587335451","https://openalex.org/W1966480196","https://openalex.org/W1974309308","https://openalex.org/W1980455776","https://openalex.org/W1990157709","https://openalex.org/W1995578999","https://openalex.org/W1997640799","https://openalex.org/W2004083707","https://openalex.org/W2021669684","https://openalex.org/W2023324267","https://openalex.org/W2029918260","https://openalex.org/W2032842253","https://openalex.org/W2038330765","https://openalex.org/W2041523977","https://openalex.org/W2062335820","https://openalex.org/W2071928229","https://openalex.org/W2147035016","https://openalex.org/W3143807873","https://openalex.org/W3214098784","https://openalex.org/W4245760166"],"related_works":["https://openalex.org/W2104620528","https://openalex.org/W140119233","https://openalex.org/W2757910772","https://openalex.org/W4249473811","https://openalex.org/W2394422079","https://openalex.org/W2025913943","https://openalex.org/W1492688905","https://openalex.org/W2524071042","https://openalex.org/W166351930","https://openalex.org/W2312674383"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"study":[4],"the":[5,8],"convergence":[6],"of":[7],"multiscale":[9],"finite":[10],"element":[11],"method":[12],"for":[13,24],"nonlinear":[14],"and":[15],"random":[16],"homogenization":[17,26],"problems.":[18],"Error":[19],"estimates":[20],"similar":[21],"to":[22],"those":[23],"linear":[25],"problems":[27],"are":[28],"obtained":[29],"here.":[30]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}