{"id":"https://openalex.org/W2048819467","doi":"https://doi.org/10.1137/130916540","title":"An Equilibrated A Posteriori Error Estimator for the Interior Penalty Discontinuous Galerkin Method","display_name":"An Equilibrated A Posteriori Error Estimator for the Interior Penalty Discontinuous Galerkin Method","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2048819467","doi":"https://doi.org/10.1137/130916540","mag":"2048819467"},"language":"en","primary_location":{"id":"doi:10.1137/130916540","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130916540","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/A5019658783","display_name":"Dietrich Braess","orcid":"https://orcid.org/0009-0007-7232-0299"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"D. Braess","raw_affiliation_strings":["Faculty of Mathematics, Ruhr-University, D-44780 Bochum, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Ruhr-University, D-44780 Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008316844","display_name":"Thomas Fraunholz","orcid":"https://orcid.org/0009-0006-1471-1454"},"institutions":[{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"T. Fraunholz","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Universitaet of Augsburg, D-86159 Augsburg, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universitaet of Augsburg, D-86159 Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105206538","display_name":"Ronald H. W. Hoppe","orcid":"https://orcid.org/0000-0003-2287-6102"},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]},{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"R. H. W. Hoppe","raw_affiliation_strings":["Department of Mathematics, University of Houston, Houston, TX 77204-3008 and Institut f\u00fcr Mathematik,","Universitaet of Augsburg, D-86159 Augsburg, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Houston, Houston, TX 77204-3008 and Institut f\u00fcr Mathematik,","institution_ids":["https://openalex.org/I44461941"]},{"raw_affiliation_string":"Universitaet of Augsburg, D-86159 Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019658783"],"corresponding_institution_ids":["https://openalex.org/I904495901"],"apc_list":null,"apc_paid":null,"fwci":1.9308,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.84684208,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"52","issue":"4","first_page":"2121","last_page":"2136"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9980000257492065,"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/T11416","display_name":"Numerical methods for differential equations","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":0.8138383626937866},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.8126979470252991},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.7502328157424927},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6987264752388},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6178497672080994},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5475783944129944},{"id":"https://openalex.org/keywords/method-of-mean-weighted-residuals","display_name":"Method of mean weighted residuals","score":0.5380563139915466},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.5366987586021423},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5260177254676819},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5014896392822266},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45654797554016113},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.41637158393859863},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.4142056405544281},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.41113996505737305},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4029375910758972},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25332164764404297},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17796066403388977},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07685106992721558}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8138383626937866},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8126979470252991},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.7502328157424927},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6987264752388},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6178497672080994},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5475783944129944},{"id":"https://openalex.org/C159674985","wikidata":"https://www.wikidata.org/wiki/Q6823718","display_name":"Method of mean weighted residuals","level":4,"score":0.5380563139915466},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.5366987586021423},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5260177254676819},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5014896392822266},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45654797554016113},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41637158393859863},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.4142056405544281},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.41113996505737305},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4029375910758972},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25332164764404297},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17796066403388977},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07685106992721558},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/130916540","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130916540","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:aleph.bib-bvb.de:BVB01-025938270","is_oa":false,"landing_page_url":"http://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/2314","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"software, multimedia"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:2314","is_oa":false,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-23141","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":"preprint"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:57997","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/57997","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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W251033174","https://openalex.org/W1524015806","https://openalex.org/W1583515859","https://openalex.org/W1852082788","https://openalex.org/W1972200842","https://openalex.org/W1980377066","https://openalex.org/W1991960225","https://openalex.org/W1999035024","https://openalex.org/W2001388972","https://openalex.org/W2010610235","https://openalex.org/W2015156185","https://openalex.org/W2034290095","https://openalex.org/W2041334110","https://openalex.org/W2056470693","https://openalex.org/W2064132581","https://openalex.org/W2073178677","https://openalex.org/W2075653737","https://openalex.org/W2103705455","https://openalex.org/W2107813568","https://openalex.org/W2121179843","https://openalex.org/W2130350269","https://openalex.org/W2153299448","https://openalex.org/W2154523804","https://openalex.org/W2155768256","https://openalex.org/W2519971170","https://openalex.org/W2562668947","https://openalex.org/W3149667697"],"related_works":["https://openalex.org/W2167521757","https://openalex.org/W4238745867","https://openalex.org/W2162026849","https://openalex.org/W2027900078","https://openalex.org/W2394687667","https://openalex.org/W1927950711","https://openalex.org/W2013813162","https://openalex.org/W2885311694","https://openalex.org/W4289702954","https://openalex.org/W1577720732"],"abstract_inverted_index":{"Interior":[0],"penalty":[1],"discontinuous":[2,122],"Galerkin":[3,123],"(IPDG)":[4],"methods":[5,45,124],"for":[6,43,81,107,119],"second":[7],"order":[8,71],"elliptic":[9],"boundary":[10],"value":[11],"problems":[12],"have":[13,46],"been":[14,47],"derived":[15,48,86],"from":[16,149],"a":[17,39,82,100,128],"mixed":[18,101],"variational":[19],"formulation":[20],"of":[21,58,72,89,139,152,176],"the":[22,55,59,64,73,90,116,121,137,140,150,153,159,162,174,177],"problem.":[23],"Numerical":[24,171],"flux":[25],"functions":[26],"across":[27],"interelement":[28],"boundaries":[29],"play":[30],"an":[31,104],"important":[32],"role":[33],"in":[34,115],"that":[35,125],"theory.":[36],"Residual":[37],"type":[38],"posteriori":[40,83],"error":[41,84],"estimators":[42,85,164],"IPDG":[44,74],"and":[49,103,110],"analyzed":[50],"by":[51,87,98],"many":[52],"authors":[53],"including":[54],"convergence":[56],"analysis":[57],"resulting":[60],"adaptive":[61],"schemes.":[62],"Typically,":[63],"effectivity":[65],"indices":[66],"deteriorate":[67],"with":[68],"increasing":[69],"polynomial":[70],"methods.":[75],"The":[76,132],"situation":[77],"is":[78],"more":[79],"favorable":[80],"means":[88],"so-called":[91],"hypercircle":[92,133],"method.":[93],"Equilibrated":[94],"fluxes":[95],"are":[96],"obtained":[97],"using":[99],"method":[102,134],"extension":[105],"operator":[106],"Brezzi--Douglas--Marini":[108],"elements,":[109],"this":[111],"can":[112,145],"be":[113,146],"done":[114],"same":[117],"way":[118],"all":[120],"fit":[126],"into":[127],"known":[129],"unified":[130],"framework.":[131],"immediately":[135],"provides":[136],"reliability":[138],"estimator,":[141],"whereas":[142],"its":[143],"efficiency":[144,151],"easily":[147],"deduced":[148],"residual":[154],"operators.":[155],"In":[156],"contrast":[157],"to":[158],"residual-type":[160],"estimators,":[161],"new":[163],"do":[165],"not":[166],"contain":[167],"unknown":[168],"generic":[169],"constants.":[170],"results":[172],"illustrate":[173],"performance":[175],"suggested":[178],"approach.":[179]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}