{"id":"https://openalex.org/W2319010918","doi":"https://doi.org/10.1515/cmam-2016-0010","title":"Reliable Averaging for the Primal Variable in the Courant FEM and Hierarchical Error Estimators on Red-Refined Meshes","display_name":"Reliable Averaging for the Primal Variable in the Courant FEM and Hierarchical Error Estimators on Red-Refined Meshes","publication_year":2016,"publication_date":"2016-03-01","ids":{"openalex":"https://openalex.org/W2319010918","doi":"https://doi.org/10.1515/cmam-2016-0010","mag":"2319010918"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2016-0010","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2016-0010","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","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/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\u00e4t zu Berlin, Unter den Linden 6, 10099 Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Humboldt-Universit\u00e4t zu Berlin, Unter den Linden 6, 10099 Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046617182","display_name":"Martin Eigel","orcid":"https://orcid.org/0000-0003-2687-4497"},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Martin Eigel","raw_affiliation_strings":["Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046617182"],"corresponding_institution_ids":["https://openalex.org/I4210092021"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01776036,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"2","first_page":"213","last_page":"230"},"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":0.9994999766349792,"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":0.9994999766349792,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9945999979972839,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9833999872207642,"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/estimator","display_name":"Estimator","score":0.9000253677368164},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7356435060501099},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.7018755078315735},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6873224377632141},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6717147827148438},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6459288597106934},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6411300897598267},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.550408661365509},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.41656625270843506},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32641464471817017},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2802305221557617},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19713333249092102},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11896979808807373},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06069496273994446}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.9000253677368164},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7356435060501099},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.7018755078315735},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6873224377632141},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6717147827148438},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6459288597106934},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6411300897598267},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.550408661365509},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.41656625270843506},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32641464471817017},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2802305221557617},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19713333249092102},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11896979808807373},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06069496273994446},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2016-0010","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2016-0010","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1601545921","display_name":null,"funder_award_id":"R31-2008-000-10049-0","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2163017860","https://openalex.org/W2121947913","https://openalex.org/W2133947431","https://openalex.org/W2490196280","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W3208509670","https://openalex.org/W2109304297","https://openalex.org/W2100864966","https://openalex.org/W2083709218"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"hierarchical":[2],"a":[3,15,84,97,118,133],"posteriori":[4,134],"error":[5,57,122,135],"estimator":[6,58,82,136],"for":[7,21,36,137],"the":[8,22,71,81,88,105,113,128,131],"first-order":[9],"finite":[10],"element":[11],"method":[12],"(FEM)":[13],"on":[14,62,74],"red-refined":[16],"triangular":[17],"mesh":[18],"is":[19,34,67,83],"presented":[20],"2D":[23],"Poisson":[24],"model":[25],"problem.":[26],"Reliability":[27],"and":[28,66,120],"efficiency":[29],"with":[30,38],"some":[31],"explicit":[32],"constant":[33],"proved":[35],"triangulations":[37],"inner":[39],"angles":[40],"smaller":[41],"than":[42],"or":[43],"equal":[44],"to":[45,117],"<m:math":[46],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[47],"<m:mfrac>":[48],"<m:mi>\u03c0</m:mi>":[49],"<m:mn>2</m:mn>":[50],"</m:mfrac>":[51],"</m:math>":[52],"${\\frac{\\pi":[53],"}{2}}$":[54],".":[55],"The":[56,78,101],"does":[59],"not":[60],"rely":[61],"any":[63,93],"saturation":[64],"assumption":[65],"valid":[68],"even":[69],"in":[70],"pre-asymptotic":[72],"regime":[73],"arbitrarily":[75],"coarse":[76],"meshes.":[77],"evaluation":[79],"of":[80,87,112,130],"simple":[85],"post-processing":[86],"piecewise":[89],"linear":[90],"FEM":[91],"without":[92],"extra":[94],"solve":[95],"plus":[96],"higher-order":[98],"approximation":[99],"term.":[100],"results":[102],"also":[103],"allow":[104],"striking":[106],"observation":[107],"that":[108],"arbitrary":[109],"local":[110],"averaging":[111],"primal":[114],"variable":[115],"leads":[116],"reliable":[119],"efficient":[121],"estimation.":[123],"Several":[124],"numerical":[125],"experiments":[126],"illustrate":[127],"performance":[129],"proposed":[132],"computational":[138],"benchmarks.":[139]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}