{"id":"https://openalex.org/W624819622","doi":"https://doi.org/10.1137/15m1026687","title":"$hp$-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems","display_name":"$hp$-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W624819622","doi":"https://doi.org/10.1137/15m1026687","mag":"624819622"},"language":"en","primary_location":{"id":"doi:10.1137/15m1026687","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1026687","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5023276584","display_name":"V\u00edt Dolej\u0161\u00ed","orcid":"https://orcid.org/0000-0001-6356-934X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V\u00edt Dolej\u0161\u00ed","raw_affiliation_strings":["Department of Numerical Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Numerical Mathematics","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061539614","display_name":"Alexandre Ern","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alexandre Ern","raw_affiliation_strings":["Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique","institution_ids":["https://openalex.org/I4210128309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020083948","display_name":"Martin Vohral\u0131\u0301k","orcid":"https://orcid.org/0000-0002-8838-7689"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Vohral\u00edk","raw_affiliation_strings":["Simulation for the Environment : Reliable and Efficient Numerical Algorithms"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Simulation for the Environment : Reliable and Efficient Numerical Algorithms","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.3373,"has_fulltext":true,"cited_by_count":52,"citation_normalized_percentile":{"value":0.98063881,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"38","issue":"5","first_page":"A3220","last_page":"A3246"},"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":0.9988999962806702,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9945999979972839,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.7965148687362671},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7611704468727112},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6112573146820068},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5932680368423462},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5092774629592896},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5090622305870056},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.48843732476234436},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4750618636608124},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4603462219238281},{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"Adaptive mesh refinement","score":0.45631229877471924},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4115433990955353},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.36762404441833496},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3340582251548767},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11428627371788025}],"concepts":[{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.7965148687362671},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7611704468727112},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6112573146820068},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5932680368423462},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5092774629592896},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5090622305870056},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.48843732476234436},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4750618636608124},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4603462219238281},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.45631229877471924},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4115433990955353},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.36762404441833496},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3340582251548767},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11428627371788025},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/15m1026687","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1026687","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01165187v3","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-01165187","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, 2016, 38 (5), pp.A3220-A3246. &#x27E8;10.1137/15M1026687&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G771398276","display_name":null,"funder_award_id":"13-00522S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G8207394792","display_name":"Guaranteed fully adaptive algorithms with tailored inexact solvers for complex porous media flows","funder_award_id":"647134","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8779444662","display_name":null,"funder_award_id":"647134 GATIPOR","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W46603733","https://openalex.org/W94458352","https://openalex.org/W181225834","https://openalex.org/W221725956","https://openalex.org/W253824085","https://openalex.org/W628726389","https://openalex.org/W1603402123","https://openalex.org/W1965820280","https://openalex.org/W1966388474","https://openalex.org/W1966768630","https://openalex.org/W1967345544","https://openalex.org/W1973168665","https://openalex.org/W1978286467","https://openalex.org/W1978548050","https://openalex.org/W1979771104","https://openalex.org/W1979783941","https://openalex.org/W1979928109","https://openalex.org/W1980377066","https://openalex.org/W1982050100","https://openalex.org/W2007289139","https://openalex.org/W2010610235","https://openalex.org/W2015156185","https://openalex.org/W2029551173","https://openalex.org/W2030028670","https://openalex.org/W2034290095","https://openalex.org/W2041334110","https://openalex.org/W2041523977","https://openalex.org/W2045214757","https://openalex.org/W2051889472","https://openalex.org/W2052385123","https://openalex.org/W2071166325","https://openalex.org/W2089907194","https://openalex.org/W2093479952","https://openalex.org/W2132509247","https://openalex.org/W2152347537","https://openalex.org/W2154523804","https://openalex.org/W2164402335","https://openalex.org/W2167521757","https://openalex.org/W2296372173","https://openalex.org/W2525823748","https://openalex.org/W2562668947","https://openalex.org/W3100812035","https://openalex.org/W3149667697"],"related_works":["https://openalex.org/W2167521757","https://openalex.org/W2298673793","https://openalex.org/W2885311694","https://openalex.org/W2013813162","https://openalex.org/W1976798187","https://openalex.org/W2963636343","https://openalex.org/W3102618207","https://openalex.org/W3098143598","https://openalex.org/W2135086547","https://openalex.org/W1598742316"],"abstract_inverted_index":{"We":[0,105],"devise":[1],"and":[2,20,51,60,100,110,132,144,167],"study":[3],"experimentally":[4],"adaptive":[5,168],"strategies":[6,113],"driven":[7],"by":[8],"a":[9,71,91,102,141,164],"posteriori":[10],"error":[11,73,84],"estimates":[12,44,109],"to":[13,81],"select":[14],"automatically":[15],"both":[16],"the":[17,21,25,97,108,115,127,157],"space":[18,33],"mesh":[19,98],"polynomial":[22,58],"degree":[23],"in":[24,31],"numerical":[26],"approximation":[27],"of":[28],"diffusion":[29],"equations":[30],"two":[32],"dimensions.":[34],"The":[35],"adaptation":[36],"is":[37,123],"based":[38],"on":[39,87,96,135,152,160],"equilibrated":[40],"flux":[41],"estimates.":[42],"These":[43],"are":[45,150],"presented":[46],"here":[47],"for":[48,55,61,125,140,156],"inhomogeneous":[49],"Dirichlet":[50],"Neumann":[52],"boundary":[53],"conditions,":[54],"spatially":[56],"varying":[57],"degree,":[59],"mixed":[62],"rectangular-triangular":[63],"grids":[64,139,155],"possibly":[65],"containing":[66],"hanging":[67],"nodes.":[68],"They":[69],"deliver":[70],"global":[72],"upper":[74],"bound":[75],"with":[76,90,101,163],"constant":[77,93],"one":[78],"and,":[79],"up":[80],"data":[82],"oscillation,":[83],"lower":[85],"bounds":[86],"element":[88],"patches":[89],"generic":[92],"dependent":[94],"only":[95],"regularity":[99],"computable":[103],"bound.":[104],"numerically":[106],"assess":[107],"several":[111,161],"$hp$-adaptive":[112],"using":[114],"interior":[116],"penalty":[117],"discontinuous":[118],"Galerkin":[119],"method.":[120],"Asymptotic":[121],"exactness":[122],"observed":[124],"all":[126],"symmetric,":[128],"nonsymmetric":[129],"(odd":[130],"degrees),":[131],"incomplete":[133,158],"variants":[134],"nonnested":[136],"unstructured":[137],"triangular":[138,154],"smooth":[142],"solution":[143,166],"uniform":[145],"refinement.":[146,169],"Exponential":[147],"convergence":[148],"rates":[149],"reported":[151],"nonmatching":[153],"version":[159],"benchmarks":[162],"singular":[165]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}
