{"id":"https://openalex.org/W1988374794","doi":"https://doi.org/10.1137/11082292x","title":"Postprocessed Two-Scale Finite Element Discretizations, Part I","display_name":"Postprocessed Two-Scale Finite Element Discretizations, Part I","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1988374794","doi":"https://doi.org/10.1137/11082292x","mag":"1988374794"},"language":"en","primary_location":{"id":"doi:10.1137/11082292x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/11082292x","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/A5100453130","display_name":"Fang Liu","orcid":"https://orcid.org/0000-0003-4256-3947"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fang Liu","raw_affiliation_strings":["fliu@lsec.cc.ac.cn#TAB#"],"affiliations":[{"raw_affiliation_string":"fliu@lsec.cc.ac.cn#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044512711","display_name":"Martin Stynes","orcid":"https://orcid.org/0000-0003-2085-7354"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Stynes","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113202217","display_name":"Aihui Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aihui Zhou","raw_affiliation_strings":["azhou@lsec.cc.ac.cn#TAB#"],"affiliations":[{"raw_affiliation_string":"azhou@lsec.cc.ac.cn#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100453130"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.07534778,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"49","issue":"5","first_page":"1947","last_page":"1971"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T10514","display_name":"Numerical methods in engineering","score":0.9976000189781189,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9973000288009644,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8009133338928223},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6756868362426758},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5406879782676697},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.49596962332725525},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.4801754057407379},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.47411301732063293},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.4645872414112091},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4279431700706482},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.41440629959106445},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4123415946960449},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36666369438171387},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3280041217803955},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10102075338363647}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8009133338928223},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6756868362426758},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5406879782676697},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.49596962332725525},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.4801754057407379},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.47411301732063293},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4645872414112091},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4279431700706482},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.41440629959106445},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4123415946960449},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36666369438171387},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3280041217803955},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10102075338363647},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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":1,"locations":[{"id":"doi:10.1137/11082292x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/11082292x","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7400000095367432,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W392395217","https://openalex.org/W1492326914","https://openalex.org/W1502072544","https://openalex.org/W1586623601","https://openalex.org/W1866311589","https://openalex.org/W1971109424","https://openalex.org/W1975238525","https://openalex.org/W1976610942","https://openalex.org/W1980455776","https://openalex.org/W1981792545","https://openalex.org/W2000371428","https://openalex.org/W2009524444","https://openalex.org/W2009985306","https://openalex.org/W2010452605","https://openalex.org/W2029191491","https://openalex.org/W2034623099","https://openalex.org/W2041523977","https://openalex.org/W2041568728","https://openalex.org/W2061937382","https://openalex.org/W2068987297","https://openalex.org/W2069961480","https://openalex.org/W2078439156","https://openalex.org/W2086268649","https://openalex.org/W2165607996","https://openalex.org/W2613213362","https://openalex.org/W3148150263","https://openalex.org/W4255975175"],"related_works":["https://openalex.org/W1968390457","https://openalex.org/W2146600718","https://openalex.org/W1912064545","https://openalex.org/W3132233781","https://openalex.org/W2138419695","https://openalex.org/W1973136543","https://openalex.org/W1990392133","https://openalex.org/W2120227340","https://openalex.org/W4238156215","https://openalex.org/W2500331132"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"a":[3,47],"simple":[4],"postprocessing":[5],"of":[6,11,74,87,108,115],"two-scale":[7,42,79],"finite":[8,80,97],"element":[9,81,98],"discretizations":[10],"elliptic":[12],"partial":[13],"differential":[14],"operators,":[15],"where":[16,57],"boundary":[17],"value":[18],"problems":[19,22],"and":[20,30,50,59,64],"eigenvalue":[21],"on":[23],"tensor-product":[24],"domains":[25],"$\\Omega\\subset\\mathbb{R}^d$":[26],"are":[27,35,61],"both":[28,72],"examined":[29],"conforming":[31],"piecewise":[32],"d-linear":[33],"elements":[34],"used.":[36],"For":[37],"$d\\geq2$,":[38],"suppose":[39],"that":[40,76],"the":[41,62,77,84,90,94,101,112,119],"method":[43],"is":[44,69],"applied":[45],"using":[46],"coarse":[48,65],"mesh":[49,66],"some":[51],"univariate":[52],"fine":[53,63],"meshes":[54],"satisfying":[55],"$H=\\mathcal{O}(h^{2/3})$,":[56],"h":[58],"H":[60],"widths.":[67],"It":[68],"shown":[70],"for":[71],"classes":[73],"problem":[75],"postprocessed":[78,95],"solution":[82,103],"achieves":[83],"same":[85],"order":[86],"accuracy":[88],"in":[89],"$H^1(\\Omega)$":[91],"norm":[92],"as":[93],"standard":[96],"solution,":[99],"but":[100],"former":[102],"uses":[104],"only":[105],"$\\mathcal{O}(h^{-(2d+1)/3})$":[106],"degrees":[107,114],"freedom":[109,116],"compared":[110],"with":[111],"$\\mathcal{O}(h^{-d})$":[113],"required":[117],"by":[118],"latter.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}