{"id":"https://openalex.org/W2092508481","doi":"https://doi.org/10.1137/s1064827502419932","title":"The Reduced Basis Element Method: Application to a Thermal Fin Problem","display_name":"The Reduced Basis Element Method: Application to a Thermal Fin Problem","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2092508481","doi":"https://doi.org/10.1137/s1064827502419932","mag":"2092508481"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827502419932","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502419932","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5089357934","display_name":"Yvon Maday","orcid":"https://orcid.org/0000-0002-0443-6544"},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Yvon Maday","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions","institution_ids":["https://openalex.org/I4210158291"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064491960","display_name":"Einar M. R\u00f8nquist","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Einar M. Ronquist","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6426,"has_fulltext":false,"cited_by_count":135,"citation_normalized_percentile":{"value":0.92460138,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"26","issue":"1","first_page":"240","last_page":"258"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9998000264167786,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.7639267444610596},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7433637976646423},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.7416055202484131},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.6598445177078247},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6379919052124023},{"id":"https://openalex.org/keywords/mortar-methods","display_name":"Mortar methods","score":0.6125109195709229},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5288492441177368},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.513873815536499},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.47495532035827637},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4663604497909546},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4500215947628021},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.44865816831588745},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4417174458503723},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4416257441043854},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4174187481403351},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38896387815475464},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3391563296318054},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27636635303497314}],"concepts":[{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.7639267444610596},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7433637976646423},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.7416055202484131},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.6598445177078247},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6379919052124023},{"id":"https://openalex.org/C97110765","wikidata":"https://www.wikidata.org/wiki/Q17099078","display_name":"Mortar methods","level":4,"score":0.6125109195709229},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5288492441177368},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.513873815536499},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.47495532035827637},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4663604497909546},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4500215947628021},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.44865816831588745},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4417174458503723},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4416257441043854},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4174187481403351},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38896387815475464},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3391563296318054},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27636635303497314},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827502419932","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502419932","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1505358753","https://openalex.org/W1545082185","https://openalex.org/W1968287676","https://openalex.org/W1991647816","https://openalex.org/W1994207073","https://openalex.org/W2067145579","https://openalex.org/W2102753028","https://openalex.org/W2161024376","https://openalex.org/W2240238749","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W286248473","https://openalex.org/W2412889084","https://openalex.org/W2092836554","https://openalex.org/W3145205507","https://openalex.org/W2059321831","https://openalex.org/W1253925978","https://openalex.org/W170868261","https://openalex.org/W2045656285","https://openalex.org/W2008273138","https://openalex.org/W1510415755"],"abstract_inverted_index":{"The":[0,31,77],"reduced":[1,28,63,100],"basis":[2,29,64],"element":[3],"method":[4,24,105],"is":[5,34,81,106],"a":[6,42,52,90,94,103,138],"new":[7],"approach":[8],"for":[9],"the":[10,21,27,37,75,87,98,110,120,123,134,148],"approximation":[11,79],"of":[12,39,44,84,122,133],"partial":[13],"differential":[14],"equations":[15],"that":[16,48,67,89,143],"takes":[17],"its":[18],"roots":[19],"in":[20,26],"domain":[22,38],"decomposition":[23],"and":[25,126,130],"discretization.":[30],"basic":[32],"idea":[33],"to":[35,51,70,93,97,108,146],"decompose":[36],"computation":[40],"into":[41],"series":[43],"subdomains":[45],"(the":[46],"elements)":[47],"are":[49,59,68],"similar":[50],"few":[53],"reference":[54,57,124],"domains.":[55],"These":[56],"domains":[58],"actually":[60],"\"filled\"":[61],"with":[62,74,86,128],"functional":[65],"spaces":[66],"mapped":[69,99],"each":[71],"subdomain":[72,95],"together":[73,127],"geometry.":[76],"discrete":[78],"space":[80],"then":[82],"composed":[83],"functions":[85],"property":[88],"function":[91],"restricted":[92],"belongs":[96],"spaces.":[101],"Finally,":[102],"mortar-type":[104],"applied":[107],"glue":[109],"various":[111],"local":[112],"functions.":[113],"In":[114],"this":[115],"paper":[116],"we":[117,136],"focus":[118],"on":[119],"definition":[121],"shapes,":[125],"theoretical":[129],"numerical":[131],"justifications":[132],"method,":[135],"provide":[137],"posteriori":[139],"error":[140],"analysis":[141],"tools":[142],"allow":[144],"us":[145],"certify":[147],"computational":[149],"results.":[150]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}