{"id":"https://openalex.org/W2074282379","doi":"https://doi.org/10.1137/130915856","title":"Discrete Reliability for Crouzeix--Raviart FEMs","display_name":"Discrete Reliability for Crouzeix--Raviart FEMs","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2074282379","doi":"https://doi.org/10.1137/130915856","mag":"2074282379"},"language":"en","primary_location":{"id":"doi:10.1137/130915856","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130915856","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":"https://research.utwente.nl/en/publications/e52cc0c8-ad0f-4b1a-aea4-679a8cb07845","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036808184","display_name":"Carsten Carstensen","orcid":null},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Carsten Carstensen","raw_affiliation_strings":["Humboldt Universit\u00e1t zu Berlin"],"affiliations":[{"raw_affiliation_string":"Humboldt Universit\u00e1t zu Berlin","institution_ids":["https://openalex.org/I39343248"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035829145","display_name":"Dietmar Gallistl","orcid":"https://orcid.org/0000-0001-8954-4175"},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Dietmar Gallistl","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Humboldt-Universit\u00e4t zu Berlin, D-10099 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Humboldt-Universit\u00e4t zu Berlin, D-10099 Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031200453","display_name":"Mira Schedensack","orcid":"https://orcid.org/0000-0003-1182-9116"},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mira Schedensack","raw_affiliation_strings":["Humboldt Universit\u00e1t zu Berlin"],"affiliations":[{"raw_affiliation_string":"Humboldt Universit\u00e1t zu Berlin","institution_ids":["https://openalex.org/I39343248"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035829145"],"corresponding_institution_ids":["https://openalex.org/I39343248"],"apc_list":null,"apc_paid":null,"fwci":2.1146,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.86510681,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"51","issue":"5","first_page":"2935","last_page":"2955"},"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":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/mathematics","display_name":"Mathematics","score":0.835990309715271},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5932838916778564},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5641047954559326},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5196501016616821},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4899443984031677},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4661957323551178},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35741856694221497},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33173996210098267},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24862131476402283},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11628970503807068}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.835990309715271},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5932838916778564},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5641047954559326},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5196501016616821},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4899443984031677},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4661957323551178},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35741856694221497},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33173996210098267},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24862131476402283},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11628970503807068},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/130915856","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130915856","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:ris.utwente.nl:openaire/e52cc0c8-ad0f-4b1a-aea4-679a8cb07845","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/e52cc0c8-ad0f-4b1a-aea4-679a8cb07845","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Carstensen, C, Gallistl, D & Schedensack, M 2013, 'Discrete reliability for Crouzeix--Raviart FEMs', SIAM journal on numerical analysis, vol. 51, no. 5, pp. 2935-2955. https://doi.org/10.1137/130915856","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:89008","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/89008","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:ris.utwente.nl:openaire/e52cc0c8-ad0f-4b1a-aea4-679a8cb07845","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/e52cc0c8-ad0f-4b1a-aea4-679a8cb07845","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Carstensen, C, Gallistl, D & Schedensack, M 2013, 'Discrete reliability for Crouzeix--Raviart FEMs', SIAM journal on numerical analysis, vol. 51, no. 5, pp. 2935-2955. https://doi.org/10.1137/130915856","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W280547473","https://openalex.org/W1557452007","https://openalex.org/W1978687734","https://openalex.org/W1979771104","https://openalex.org/W2008916847","https://openalex.org/W2020294233","https://openalex.org/W2023070026","https://openalex.org/W2029129352","https://openalex.org/W2035654636","https://openalex.org/W2036607335","https://openalex.org/W2044959876","https://openalex.org/W2053482768","https://openalex.org/W2058824833","https://openalex.org/W2063856293","https://openalex.org/W2064991465","https://openalex.org/W2071902409","https://openalex.org/W2072811159","https://openalex.org/W2083317712","https://openalex.org/W2084743165","https://openalex.org/W2096545304","https://openalex.org/W2105551156","https://openalex.org/W2107813568","https://openalex.org/W2124199582","https://openalex.org/W2137365186","https://openalex.org/W2140677965","https://openalex.org/W2151369319","https://openalex.org/W2157129549","https://openalex.org/W2312327245","https://openalex.org/W2317856682","https://openalex.org/W3085068140"],"related_works":["https://openalex.org/W4287880334","https://openalex.org/W4366700029","https://openalex.org/W3175363083","https://openalex.org/W4285230481","https://openalex.org/W4385769873","https://openalex.org/W2015759683","https://openalex.org/W4281634296","https://openalex.org/W4319161863","https://openalex.org/W2371687270","https://openalex.org/W2898674639"],"abstract_inverted_index":{"The":[0],"proof":[1,84],"of":[2,6,15,45,68],"optimal":[3],"convergence":[4],"rates":[5],"adaptive":[7],"finite":[8,29],"element":[9,30],"methods":[10],"relies":[11],"on":[12,32,57],"Stevenson's":[13],"concept":[14],"discrete":[16,23,42,91],"reliability.":[17],"This":[18,90],"paper":[19,80],"proves":[20],"the":[21,26,55,66,69,82,96],"general":[22],"reliability":[24,92,94],"for":[25,85,95,108],"nonconforming":[27],"Crouzeix--Raviart":[28],"method":[31],"multiply":[33,76,109],"connected":[34,77,110],"domains":[35],"in":[36,103],"any":[37,62,73,104],"space":[38,105],"dimension.":[39],"A":[40],"novel":[41],"quasi-interpolation":[43],"operator":[44],"first-order":[46],"approximation":[47],"involves":[48],"an":[49],"intermediate":[50],"triangulation":[51],"and":[52,75,107],"acts":[53],"as":[54],"identity":[56],"unrefined":[58],"simplices,":[59],"to":[60,72],"circumvent":[61],"Helmholtz":[63],"decomposition.":[64],"Besides":[65],"generalization":[67],"known":[70],"application":[71],"dimension":[74,106],"domains,":[78],"this":[79],"outlines":[81],"optimality":[83],"uniformly":[86],"convex":[87],"minimization":[88],"problems.":[89],"implies":[93],"explicit":[97],"residual-based":[98],"a":[99],"posteriori":[100],"error":[101],"estimator":[102],"domains.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4}],"updated_date":"2026-04-22T08:38:42.863108","created_date":"2025-10-10T00:00:00"}
