{"id":"https://openalex.org/W2069156483","doi":"https://doi.org/10.1515/156939503766614126","title":"Duality-based adaptivity in the hp-finite element method","display_name":"Duality-based adaptivity in the hp-finite element method","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2069156483","doi":"https://doi.org/10.1515/156939503766614126","mag":"2069156483"},"language":"en","primary_location":{"id":"doi:10.1515/156939503766614126","is_oa":false,"landing_page_url":"https://doi.org/10.1515/156939503766614126","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"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":"Journal of Numerical 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/A5058920681","display_name":"Vincent Heuveline","orcid":"https://orcid.org/0000-0002-2217-7558"},"institutions":[{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"V. Heuveline","raw_affiliation_strings":["Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Heidelberg, INF 293, D-69120 Heidelberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Heidelberg, INF 293, D-69120 Heidelberg, Germany","institution_ids":["https://openalex.org/I223822909"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024221693","display_name":"Rolf Rannacher","orcid":null},"institutions":[{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"R. Rannacher","raw_affiliation_strings":["Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Heidelberg, INF 293, D-69120 Heidelberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Heidelberg, INF 293, D-69120 Heidelberg, Germany","institution_ids":["https://openalex.org/I223822909"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I223822909"],"apc_list":null,"apc_paid":null,"fwci":5.6436,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.96178312,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"11","issue":"2","first_page":null,"last_page":null},"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":0.9997000098228455,"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":0.9984999895095825,"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":0.8562971949577332},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7583626508712769},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.7476706504821777},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.733469545841217},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7261232137680054},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.5993905663490295},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5911189913749695},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5414597392082214},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4661639332771301},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4320474863052368},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4038873612880707},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.306435227394104},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20732331275939941},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11473312973976135}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8562971949577332},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7583626508712769},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.7476706504821777},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.733469545841217},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7261232137680054},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.5993905663490295},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5911189913749695},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5414597392082214},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4661639332771301},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4320474863052368},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4038873612880707},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.306435227394104},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20732331275939941},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11473312973976135},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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":2,"locations":[{"id":"doi:10.1515/156939503766614126","is_oa":false,"landing_page_url":"https://doi.org/10.1515/156939503766614126","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"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":"Journal of Numerical Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.2.6776","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.6776","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.iwr.uni-heidelberg.de/sfb359/PP/Preprint2003-09.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W94458352","https://openalex.org/W1492326914","https://openalex.org/W1979510989","https://openalex.org/W2068728923","https://openalex.org/W2071166325","https://openalex.org/W2133147107","https://openalex.org/W2312543728","https://openalex.org/W2487440882","https://openalex.org/W3046101478","https://openalex.org/W4245582577"],"related_works":["https://openalex.org/W2272336017","https://openalex.org/W2120874885","https://openalex.org/W2167521757","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2013813162","https://openalex.org/W2885311694","https://openalex.org/W4289702954","https://openalex.org/W2963636343","https://openalex.org/W2040975642"],"abstract_inverted_index":{"In":[0],"this":[1,64],"paper":[2],"a":[3,5],"duality-based":[4],"posteriori":[6],"error":[7,33,41],"analysis":[8],"is":[9,66],"developed":[10],"for":[11,46],"the":[12,32,47,51,56],"conforming":[13],"hp":[14],"Galerkin":[15,27],"finite":[16],"element":[17],"approximation":[18],"of":[19,31,37,50,63],"second-order":[20],"elliptic":[21],"problems.":[22],"Duality":[23],"arguments":[24],"combined":[25],"with":[26],"orthogonality":[28],"yield":[29],"representations":[30],"in":[34],"arbitrary":[35],"quantities":[36],"interest.":[38],"From":[39],"these":[40],"estimates,":[42],"criteria":[43],"are":[44],"derived":[45],"simultaneous":[48],"adaptation":[49],"mesh":[52],"size":[53],"h":[54],"and":[55],"polynomial":[57],"degree":[58],"p":[59],".":[60],"The":[61],"effectivity":[62],"procedure":[65],"confirmed":[67],"by":[68],"numerical":[69],"tests.":[70]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}