{"id":"https://openalex.org/W2126165061","doi":"https://doi.org/10.1137/040610064","title":"Localized pointwise a posteriori error estimates for gradients of piecewise linear finite element approximations to second-order quasilinear elliptic problems","display_name":"Localized pointwise a posteriori error estimates for gradients of piecewise linear finite element approximations to second-order quasilinear elliptic problems","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2126165061","doi":"https://doi.org/10.1137/040610064","mag":"2126165061"},"language":"en","primary_location":{"id":"doi:10.1137/040610064","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040610064","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/A5070767719","display_name":"Alan Demlow","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alan Demlow","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070767719"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6978,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.84525885,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"44","issue":"2","first_page":"494","last_page":"514"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994999766349792,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8734796047210693},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.8162453770637512},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6617685556411743},{"id":"https://openalex.org/keywords/nabla-symbol","display_name":"Nabla symbol","score":0.6166802048683167},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6093704700469971},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5956634283065796},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5328348875045776},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5326228737831116},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.47888511419296265},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4711764454841614},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4708045721054077},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.464726984500885},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.44467073678970337},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4395171105861664},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.4142153561115265},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.31915414333343506},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1593322455883026}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8734796047210693},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8162453770637512},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6617685556411743},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.6166802048683167},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6093704700469971},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5956634283065796},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5328348875045776},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5326228737831116},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.47888511419296265},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4711764454841614},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4708045721054077},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.464726984500885},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.44467073678970337},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4395171105861664},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.4142153561115265},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.31915414333343506},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1593322455883026},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/040610064","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040610064","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:CiteSeerX.psu:10.1.1.530.7714","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.530.7714","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ms.uky.edu/~demlow/pubs/SNA000494.pdf","raw_type":"text"},{"id":"pmh:oai:freidok.uni-freiburg.de:57166","is_oa":false,"landing_page_url":"https://freidok.uni-freiburg.de/data/57166","pdf_url":null,"source":{"id":"https://openalex.org/S4306401057","display_name":"FreiDok plus (Universit\u00e4tsbibliothek Freiburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I161046081","host_organization_name":"University of Freiburg","host_organization_lineage":["https://openalex.org/I161046081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Preprint Fakult\u00e4t f\u00fcr Mathematik und Physik, Universit\u00e4t Freiburg. - 04-17 (2004)","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1586623601","https://openalex.org/W1989665919","https://openalex.org/W2007751122","https://openalex.org/W2009985306","https://openalex.org/W2010332082","https://openalex.org/W2014371614","https://openalex.org/W2020854958","https://openalex.org/W2038490905","https://openalex.org/W2041276770","https://openalex.org/W2044300169","https://openalex.org/W2044627846","https://openalex.org/W2049473070","https://openalex.org/W2053695265","https://openalex.org/W2069048447","https://openalex.org/W2076458295","https://openalex.org/W2077174190","https://openalex.org/W2079626492","https://openalex.org/W2081210755","https://openalex.org/W2133147107","https://openalex.org/W2381246980","https://openalex.org/W4205289336"],"related_works":["https://openalex.org/W2229925025","https://openalex.org/W1539596337","https://openalex.org/W33469805","https://openalex.org/W1855007440","https://openalex.org/W1848433776","https://openalex.org/W2626435100","https://openalex.org/W1741018519","https://openalex.org/W1524084927","https://openalex.org/W1967205757","https://openalex.org/W1966487117"],"abstract_inverted_index":{"Two":[0],"types":[1],"of":[2,12,16,53,64,81,108,151],"pointwise":[3],"a":[4,38,68,70,78,99,142],"posteriori":[5,71],"error":[6,96],"estimates":[7,80,111,129],"are":[8,112],"presented":[9],"for":[10,114],"gradients":[11],"finite":[13],"element":[14],"approximations":[15],"second-order":[17],"quasilinear":[18],"elliptic":[19],"Dirichlet":[20],"boundary":[21],"value":[22],"problems":[23],"over":[24,61],"convex":[25],"polyhedral":[26],"domains":[27],"$\\Omega$":[28],"in":[29,98,127,136,141],"space":[30],"dimension":[31],"n":[32],"\\ge":[33],"2.":[34],"We":[35],"first":[36],"give":[37],"residual":[39,54],"estimator":[40,55,84],"which":[41,103,118,144],"is":[42,56,67,85],"equivalent":[43,89],"to":[44,47,58,73,87,91,94],"\\|\\nabla(u-u_h)\\|_{L_\\infty(\\Omega)":[45],"up":[46],"higher-order":[48,92],"terms.":[49],"The":[50,125],"second":[51],"type":[52],"designed":[57],"control":[59],"\\nabla(u-u_h)locally":[60],"any":[62],"subdomain":[63,107],"$\\Omega$.":[65],"It":[66],"novel":[69],"counterpart":[72],"the":[74,95,106,128,132,137,149],"localized":[75],"or":[76],"weighted":[77,100],"priori":[79],"[Sch98].":[82],"This":[83],"shown":[86],"be":[88,120],"(up":[90],"terms)":[93],"measured":[97],"global":[101],"norm":[102],"depends":[104],"on":[105,131,148],"interest.":[109],"All":[110],"proved":[113],"general":[115],"shape-regular":[116],"meshes":[117],"may":[119],"highly":[121],"graded":[122],"and":[123],"unstructured.":[124],"constants":[126],"depend":[130],"unknown":[133],"solution":[134],"u":[135],"nonlinear":[138],"case,":[139],"but":[140],"fashion":[143],"places":[145],"minimal":[146],"restrictions":[147],"regularity":[150],"u.":[152]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}