{"id":"https://openalex.org/W2036776030","doi":"https://doi.org/10.1137/s0036142903433807","title":"A Div-Curl Lemma for Edge Elements","display_name":"A Div-Curl Lemma for Edge Elements","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2036776030","doi":"https://doi.org/10.1137/s0036142903433807","mag":"2036776030"},"language":"de","primary_location":{"id":"doi:10.1137/s0036142903433807","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903433807","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10852/10659","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006596455","display_name":"Snorre H. Christiansen","orcid":"https://orcid.org/0000-0001-7618-9514"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Snorre H. Christiansen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006596455"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0099,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.77130927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"43","issue":"1","first_page":"116","last_page":"126"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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":0.9998999834060669,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8803237676620483},{"id":"https://openalex.org/keywords/curl","display_name":"Curl (programming language)","score":0.8405798673629761},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6627069711685181},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4906805753707886},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4828113317489624},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4535376727581024},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.4390571713447571},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4315441846847534},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4048049747943878},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1650526225566864}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8803237676620483},{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.8405798673629761},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6627069711685181},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4906805753707886},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4828113317489624},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4535376727581024},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.4390571713447571},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4315441846847534},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4048049747943878},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1650526225566864},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/s0036142903433807","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903433807","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:www.duo.uio.no:10852/10659","is_oa":true,"landing_page_url":"http://hdl.handle.net/10852/10659","pdf_url":null,"source":{"id":"https://openalex.org/S4306401717","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/report"}],"best_oa_location":{"id":"pmh:oai:www.duo.uio.no:10852/10659","is_oa":true,"landing_page_url":"http://hdl.handle.net/10852/10659","pdf_url":null,"source":{"id":"https://openalex.org/S4306401717","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/report"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W90066227","https://openalex.org/W136185420","https://openalex.org/W141261258","https://openalex.org/W177735991","https://openalex.org/W1516283755","https://openalex.org/W1516320851","https://openalex.org/W1522101954","https://openalex.org/W1522382323","https://openalex.org/W1533613088","https://openalex.org/W1575147392","https://openalex.org/W1582706191","https://openalex.org/W1582734821","https://openalex.org/W1595515622","https://openalex.org/W1604809219","https://openalex.org/W1674659126","https://openalex.org/W1708679080","https://openalex.org/W1852082788","https://openalex.org/W1973835324","https://openalex.org/W1989748191","https://openalex.org/W1999447349","https://openalex.org/W2000554621","https://openalex.org/W2008193785","https://openalex.org/W2010076994","https://openalex.org/W2012061418","https://openalex.org/W2015148405","https://openalex.org/W2017938125","https://openalex.org/W2053465967","https://openalex.org/W2062618977","https://openalex.org/W2064909895","https://openalex.org/W2071704402","https://openalex.org/W2083282315","https://openalex.org/W2115094993","https://openalex.org/W2143783905","https://openalex.org/W2161722781","https://openalex.org/W2596393192","https://openalex.org/W2794597669","https://openalex.org/W3021722416","https://openalex.org/W3038830718","https://openalex.org/W3039083618","https://openalex.org/W3046457476","https://openalex.org/W3149667697","https://openalex.org/W4210970781","https://openalex.org/W4242693732","https://openalex.org/W4252104256"],"related_works":["https://openalex.org/W2382844561","https://openalex.org/W2083529992","https://openalex.org/W816511862","https://openalex.org/W2238883956","https://openalex.org/W2121543990","https://openalex.org/W2402800040","https://openalex.org/W2000020320","https://openalex.org/W4252969132","https://openalex.org/W2643941443","https://openalex.org/W3097726068"],"abstract_inverted_index":{"A":[0],"variant":[1],"of":[2,19,22,46,50,54,80,89],"Murat":[3],"and":[4,10,85],"Tartar's":[5],"div-curl":[6],"lemma":[7],"is":[8],"stated":[9],"proved":[11],"for":[12],"N\u00e9d\u00e9lec's":[13],"edge":[14],"elements.":[15],"Given":[16],"two":[17],"sequences":[18,52],"vector":[20,81],"fields":[21,58],"this":[23],"type,":[24],"converging":[25],"weakly":[26],"in":[27,43,66],"L2":[28],"as":[29],"the":[30,44,51,60],"mesh":[31],"width":[32],"tends":[33],"to":[34,76],"0,":[35],"we":[36],"prove":[37],"that":[38],"their":[39],"scalar":[40,90],"product":[41],"converges":[42],"sense":[45],"distributions":[47],"when":[48],"one":[49],"consists":[53],"so-called":[55],"discrete":[56,77],"divergence-free":[57],"whereas":[59],"other":[61],"has":[62],"relatively":[63],"compact":[64],"$\\curl$":[65],"H-1.":[67],"The":[68],"proof":[69],"uses":[70],"a":[71,86],"uniform":[72],"norm":[73],"equivalence":[74],"related":[75],"compactness":[78],"properties":[79],"finite":[82,91],"element":[83,92],"spaces":[84],"super-approximation":[87],"property":[88],"spaces.":[93]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}