{"id":"https://openalex.org/W3204170665","doi":"https://doi.org/10.1090/mcom/3673","title":"Stable broken \ud835\udc3b(]olf) polynomial extensions and j-robust a posteriori error estimates by broken patchwise equilibration for the curl\u2013curl problem","display_name":"Stable broken \ud835\udc3b(]olf) polynomial extensions and j-robust a posteriori error estimates by broken patchwise equilibration for the curl\u2013curl problem","publication_year":2021,"publication_date":"2021-09-28","ids":{"openalex":"https://openalex.org/W3204170665","doi":"https://doi.org/10.1090/mcom/3673","mag":"3204170665"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3673","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3673","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5061926880","display_name":"Th\u00e9ophile Chaumont-Frelet","orcid":"https://orcid.org/0000-0002-6210-0774"},"institutions":[{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]},{"id":"https://openalex.org/I4210112930","display_name":"Laboratoire Jean-Alexandre Dieudonn\u00e9","ror":"https://ror.org/0274zdr66","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I201841394","https://openalex.org/I4210112930","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I4210117840","display_name":"Institut de Biologie Valrose","ror":"https://ror.org/03bnma344","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I154526488","https://openalex.org/I201841394","https://openalex.org/I4210096427","https://openalex.org/I4210117840"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"T. Chaumont-Frelet","raw_affiliation_strings":["Inria, 2004 Route des Lucioles, 06902 Valbonne, France; and Laboratoire J.A. Dieudonn\u00c3\u00a9, Parc Valrose, 28 Avenue Valrose, 06108 Nice, France","ATLANTIS - Mod\u00e9lisation et m\u00e9thodes num\u00e9riques pour le calcul d'interactions onde-mati\u00e8re nanostructur\u00e9e (2004 route des Lucioles BP 93 06902 Sophia Antipolis  - France)","LJAD - Laboratoire Jean Alexandre Dieudonn\u00e9 (Universit\u00e9 C\u00f4te d'Azur U.M.R. no 7351 du C.N.R.S. Parc Valrose 06108 Nice Cedex 02 France - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inria, 2004 Route des Lucioles, 06902 Valbonne, France; and Laboratoire J.A. Dieudonn\u00c3\u00a9, Parc Valrose, 28 Avenue Valrose, 06108 Nice, France","institution_ids":["https://openalex.org/I4210117840"]},{"raw_affiliation_string":"ATLANTIS - Mod\u00e9lisation et m\u00e9thodes num\u00e9riques pour le calcul d'interactions onde-mati\u00e8re nanostructur\u00e9e (2004 route des Lucioles BP 93 06902 Sophia Antipolis  - France)","institution_ids":[]},{"raw_affiliation_string":"LJAD - Laboratoire Jean Alexandre Dieudonn\u00e9 (Universit\u00e9 C\u00f4te d'Azur U.M.R. no 7351 du C.N.R.S. Parc Valrose 06108 Nice Cedex 02 France - France)","institution_ids":["https://openalex.org/I4210112930","https://openalex.org/I201841394"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061539614","display_name":"Alexandre Ern","orcid":null},"institutions":[{"id":"https://openalex.org/I142631665","display_name":"\u00c9cole nationale des ponts et chauss\u00e9es","ror":"https://ror.org/02nwvxz07","country_code":"FR","type":"education","lineage":["https://openalex.org/I142631665","https://openalex.org/I4210145102"]},{"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":"A. Ern","raw_affiliation_strings":["CERMICS, Ecole des Ponts, 77455 Marne-la-Valle, France; and Inria, 2 rue Simone Iff, 75589 Paris, France","CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CERMICS, Ecole des Ponts, 77455 Marne-la-Valle, France; and Inria, 2 rue Simone Iff, 75589 Paris, France","institution_ids":["https://openalex.org/I142631665","https://openalex.org/I4210128309"]},{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]},{"raw_affiliation_string":"SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms (France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020083948","display_name":"Martin Vohral\u0131\u0301k","orcid":"https://orcid.org/0000-0002-8838-7689"},"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":"M. Vohral\u00edk","raw_affiliation_strings":["SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms (France)","CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms (France)","institution_ids":[]},{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6333,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.81188749,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"91","issue":"333","first_page":"37","last_page":"74"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9994000196456909,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987000226974487,"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/T10635","display_name":"Hydraulic Fracturing and Reservoir Analysis","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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":0.6056084036827087},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4832656979560852},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39076098799705505},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38739675283432007},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29973018169403076}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6056084036827087},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4832656979560852},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39076098799705505},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38739675283432007},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29973018169403076}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3673","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3673","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6937939994","display_name":null,"funder_award_id":"647134","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"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":59,"referenced_works":["https://openalex.org/W66017884","https://openalex.org/W136185420","https://openalex.org/W143597873","https://openalex.org/W617113334","https://openalex.org/W1514392632","https://openalex.org/W1582734821","https://openalex.org/W1674659126","https://openalex.org/W1881147112","https://openalex.org/W1965820280","https://openalex.org/W1968082158","https://openalex.org/W1969923739","https://openalex.org/W1970198065","https://openalex.org/W1971606961","https://openalex.org/W1980377066","https://openalex.org/W2015442042","https://openalex.org/W2032997846","https://openalex.org/W2039924562","https://openalex.org/W2051889472","https://openalex.org/W2062618977","https://openalex.org/W2065700840","https://openalex.org/W2070623505","https://openalex.org/W2076914242","https://openalex.org/W2080408545","https://openalex.org/W2089907194","https://openalex.org/W2135299604","https://openalex.org/W2143783905","https://openalex.org/W2154523804","https://openalex.org/W2164341773","https://openalex.org/W2164402335","https://openalex.org/W2167521757","https://openalex.org/W2170299747","https://openalex.org/W2473389504","https://openalex.org/W2562668947","https://openalex.org/W2577131966","https://openalex.org/W2780989679","https://openalex.org/W2785556939","https://openalex.org/W2897494856","https://openalex.org/W2914105805","https://openalex.org/W2952659859","https://openalex.org/W2963610501","https://openalex.org/W2969685607","https://openalex.org/W2971995543","https://openalex.org/W3016802769","https://openalex.org/W3035086458","https://openalex.org/W3046457476","https://openalex.org/W3100812035","https://openalex.org/W3118427563","https://openalex.org/W3129604430","https://openalex.org/W3157145968","https://openalex.org/W3192063817","https://openalex.org/W4205815276","https://openalex.org/W4234002930","https://openalex.org/W4239704419","https://openalex.org/W4240668518","https://openalex.org/W4242885417","https://openalex.org/W4252104256","https://openalex.org/W4290828441","https://openalex.org/W4387725342","https://openalex.org/W6619313113"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793"],"abstract_inverted_index":{"We":[0,16,105],"study":[1],"extensions":[2],"of":[3,11,101,110,119,128,206],"piecewise":[4,26,38],"polynomial":[5,27,103],"data":[6],"prescribed":[7,30,37],"in":[8,19,40,44,150],"a":[9,115,145,155,210],"patch":[10,207],"tetrahedra":[12,213],"sharing":[13],"an":[14],"edge.":[15,217],"show":[17],"stability":[18],"the":[20,23,45,50,53,90,102,108,114,120,224,234],"sense":[21],"that":[22],"minimizers":[24,51],"over":[25,52],"spaces":[28],"with":[29,89,124],"tangential":[31],"component":[32],"jumps":[33],"across":[34],"faces":[35],"and":[36,97,139,200],"curl":[39],"elements":[41,127],"are":[42,95,134,142],"subordinate":[43],"broken":[46,54,146],"energy":[47],"norm":[48],"to":[49,113,197],"<inline-formula":[55,157],"content-type=\"math/mathml\">":[56,158],"<mml:math":[57,159],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[58,160],"alttext=\"bold-italic":[59,161],"upper":[60,162],"H":[61,163],"left-parenthesis":[62,164],"bold":[63,165],"c":[64,166],"u":[65,167],"r":[66,168],"l":[67,169],"right-parenthesis\">":[68,170],"<mml:semantics>":[69,171],"<mml:mrow>":[70,172],"<mml:mi":[71,75,173,177],"mathvariant=\"bold-italic\">H</mml:mi>":[72,174],"<mml:mo":[73,77,175,179],"stretchy=\"false\">(</mml:mo>":[74,176],"mathvariant=\"bold\">curl</mml:mi>":[76,178],"stretchy=\"false\">)</mml:mo>":[78,180],"</mml:mrow>":[79,181],"<mml:annotation":[80,182],"encoding=\"application/x-tex\">\\boldsymbol":[81,183],"H(\\boldsymbol":[82,184],"{\\operatorname":[83,185],"{curl}})</mml:annotation>":[84,186],"</mml:semantics>":[85,187],"</mml:math>":[86,188],"</inline-formula>":[87,189],"space":[88],"same":[91],"prescriptions.":[92],"Our":[93],"proofs":[94],"constructive":[96],"yield":[98],"constants":[99],"independent":[100],"degree.":[104],"then":[106],"detail":[107],"application":[109],"this":[111],"result":[112],"posteriori":[116],"error":[117,219],"analysis":[118],"curl\u2013curl":[121],"problem":[122],"discretized":[123],"N\u00e9d\u00e9lec":[125],"finite":[126],"arbitrary":[129],"order.":[130],"The":[131,192,218],"resulting":[132],"estimators":[133],"reliable,":[135],"locally":[136],"efficient,":[137],"polynomial-degree-robust,":[138],"inexpensive.":[140],"They":[141],"constructed":[143],"by":[144,209],"patchwise":[147],"equilibration":[148,193],"which,":[149],"particular,":[151],"does":[152],"not":[153],"produce":[154],"globally":[156],"-conforming":[190],"flux.":[191],"is":[194,228],"only":[195],"related":[196],"edge":[198],"patches":[199],"can":[201],"be":[202],"realized":[203],"without":[204],"solutions":[205],"problems":[208],"sweep":[211],"through":[212],"around":[214],"every":[215],"mesh":[216],"estimates":[220],"become":[221],"guaranteed":[222],"when":[223],"regularity":[225],"pick-up":[226],"constant":[227],"explicitly":[229],"known.":[230],"Numerical":[231],"experiments":[232],"illustrate":[233],"theoretical":[235],"findings.":[236]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-23T13:55:30.953635","created_date":"2021-10-11T00:00:00"}