{"id":"https://openalex.org/W3087944997","doi":"https://doi.org/10.1137/20m137121x","title":"Optimal Convergence Rates for Elliptic Homogenization Problems in Nondivergence-Form: Analysis and Numerical Illustrations","display_name":"Optimal Convergence Rates for Elliptic Homogenization Problems in Nondivergence-Form: Analysis and Numerical Illustrations","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3087944997","doi":"https://doi.org/10.1137/20m137121x","mag":"3087944997"},"language":"en","primary_location":{"id":"doi:10.1137/20m137121x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m137121x","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2009.11259","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012920876","display_name":"Timo Sprekeler","orcid":"https://orcid.org/0000-0003-2934-8126"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Timo Sprekeler","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2934-8126","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078512465","display_name":"Hung V. Tran","orcid":"https://orcid.org/0000-0002-9244-3823"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hung V. Tran","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-9244-3823","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012920876"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3028,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58198148,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"19","issue":"3","first_page":"1453","last_page":"1473"},"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":0.9997000098228455,"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/hessian-matrix","display_name":"Hessian matrix","score":0.9323837757110596},{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.8647323846817017},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7145788073539734},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6210059523582458},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.598054051399231},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5158182978630066},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5125067234039307},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4754350185394287},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.4709906280040741},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4621966481208801},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.45978856086730957},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.41203057765960693},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.34712332487106323},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.34324437379837036},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19013312458992004},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13290411233901978},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07836192846298218}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.9323837757110596},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.8647323846817017},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7145788073539734},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6210059523582458},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.598054051399231},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5158182978630066},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5125067234039307},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4754350185394287},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.4709906280040741},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4621966481208801},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.45978856086730957},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.41203057765960693},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.34712332487106323},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.34324437379837036},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19013312458992004},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13290411233901978},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07836192846298218},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","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},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"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/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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m137121x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m137121x","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:2009.11259","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2009.11259","pdf_url":"https://arxiv.org/pdf/2009.11259","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"},{"id":"mag:3087944997","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2009.11259","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2009.11259","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2009.11259","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2009.11259","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2009.11259","pdf_url":"https://arxiv.org/pdf/2009.11259","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/G1327798365","display_name":"EPSRC Centre for Doctoral Training in Partial Differential Equations: Analysis and Applications","funder_award_id":"EP/L015811/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5118787699","display_name":null,"funder_award_id":"DMS-1664424","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5812500744","display_name":null,"funder_award_id":"DMS-1843320","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"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1478805268","https://openalex.org/W1515685921","https://openalex.org/W1547249381","https://openalex.org/W1866311589","https://openalex.org/W1938238307","https://openalex.org/W1972877576","https://openalex.org/W1973700156","https://openalex.org/W1983836181","https://openalex.org/W1984465228","https://openalex.org/W1987171839","https://openalex.org/W1987461346","https://openalex.org/W1987581101","https://openalex.org/W1990157709","https://openalex.org/W2004345879","https://openalex.org/W2015354363","https://openalex.org/W2029918260","https://openalex.org/W2030134333","https://openalex.org/W2038667362","https://openalex.org/W2051591931","https://openalex.org/W2060581458","https://openalex.org/W2072853909","https://openalex.org/W2078320270","https://openalex.org/W2082187902","https://openalex.org/W2097837019","https://openalex.org/W2103449449","https://openalex.org/W2111062239","https://openalex.org/W2125887644","https://openalex.org/W2137746982","https://openalex.org/W2138940269","https://openalex.org/W2488772071","https://openalex.org/W2963905835","https://openalex.org/W2963925845","https://openalex.org/W2996935071","https://openalex.org/W3039654572","https://openalex.org/W3089838140","https://openalex.org/W3099147018"],"related_works":["https://openalex.org/W2953831595","https://openalex.org/W3114282706","https://openalex.org/W2278937105","https://openalex.org/W3105809284","https://openalex.org/W2329790770","https://openalex.org/W2990187152","https://openalex.org/W2061969432","https://openalex.org/W3082555402","https://openalex.org/W2002935642","https://openalex.org/W2969645020","https://openalex.org/W2790726926","https://openalex.org/W2524953147","https://openalex.org/W1503761432","https://openalex.org/W2038099278","https://openalex.org/W2095140771","https://openalex.org/W2016639867","https://openalex.org/W2071345466","https://openalex.org/W2165630134","https://openalex.org/W2952068648","https://openalex.org/W2904244000"],"abstract_inverted_index":{"We":[0,27,51,68],"study":[1],"optimal":[2,31,54],"convergence":[3,35],"rates":[4],"in":[5,46,65],"the":[6,14,30,34,39,42,47,66,86,89],"periodic":[7],"homogenization":[8],"of":[9,13,36,41,88],"linear":[10],"elliptic":[11],"equations":[12],"form":[15],"$-A(x/\\varepsilon):D^2":[16],"u^{\\varepsilon}":[17],"=":[18],"f$":[19],"subject":[20],"to":[21,38,79],"a":[22],"homogeneous":[23],"Dirichlet":[24],"boundary":[25],"condition.":[26],"show":[28],"that":[29],"rate":[32],"for":[33],"$u^{\\varepsilon}$":[37],"solution":[40],"corresponding":[43],"homogenized":[44],"problem":[45],"$W^{1,p}$-norm":[48],"is":[49],"$\\mathcal{O}(\\varepsilon)$.":[50],"further":[52],"obtain":[53],"gradient":[55],"and":[56,76],"Hessian":[57],"bounds":[58],"with":[59],"correction":[60],"terms":[61],"taken":[62],"into":[63],"account":[64],"$L^p$-norm.":[67],"then":[69],"provide":[70],"an":[71],"explicit":[72],"$c$-bad":[73],"diffusion":[74],"matrix":[75],"use":[77],"it":[78],"perform":[80],"various":[81],"numerical":[82],"experiments,":[83],"which":[84],"demonstrate":[85],"optimality":[87],"obtained":[90],"rates.":[91]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
