{"id":"https://openalex.org/W2001775732","doi":"https://doi.org/10.1137/s0036142901391128","title":"hp-Approximation Theory forBDFMandRTFinite Elements on Quadrilaterals","display_name":"hp-Approximation Theory forBDFMandRTFinite Elements on Quadrilaterals","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2001775732","doi":"https://doi.org/10.1137/s0036142901391128","mag":"2001775732"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901391128","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5091196582","display_name":"Mark Ainsworth","orcid":"https://orcid.org/0000-0002-4899-1048"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mark Ainsworth","raw_affiliation_strings":["Mathematics And Statistics"],"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014464208","display_name":"Katia Pinchedez","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Katia Pinchedez","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.242,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":27,"citation_normalized_percentile":{"value":0.883727,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":88},"biblio":{"volume":"40","issue":"6","first_page":"2047","last_page":"2068"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998,"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":0.9998,"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":0.9988,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quadrilateral","display_name":"Quadrilateral","score":0.7065245}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.78397506},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7352197},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.7065245},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6399205},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6088841},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5852972},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.56648374},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4873832},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.463943},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.44153827},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37118095},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21888974},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08006418},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901391128","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":27,"referenced_works":["https://openalex.org/W1502992081","https://openalex.org/W1984700181","https://openalex.org/W1985861577","https://openalex.org/W1989700911","https://openalex.org/W2009674606","https://openalex.org/W2015804955","https://openalex.org/W2041523977","https://openalex.org/W2054810687","https://openalex.org/W2062618977","https://openalex.org/W2062969160","https://openalex.org/W2066450870","https://openalex.org/W2071166325","https://openalex.org/W2072236487","https://openalex.org/W2077244888","https://openalex.org/W2080102458","https://openalex.org/W2082721974","https://openalex.org/W2094695561","https://openalex.org/W2122710352","https://openalex.org/W2124387207","https://openalex.org/W2125667158","https://openalex.org/W2473701906","https://openalex.org/W2596290099","https://openalex.org/W3130571686","https://openalex.org/W3149667697","https://openalex.org/W396760590","https://openalex.org/W4206477975","https://openalex.org/W4256651668"],"related_works":["https://openalex.org/W789026155","https://openalex.org/W4231998818","https://openalex.org/W4225381306","https://openalex.org/W2953041517","https://openalex.org/W2898882437","https://openalex.org/W2352017532","https://openalex.org/W2164512662","https://openalex.org/W2077820952","https://openalex.org/W2027181523","https://openalex.org/W1968844089"],"abstract_inverted_index":{"We":[0],"study":[1],"approximation":[2],"properties":[3],"of":[4,8,40,67,73,90,96,106],"hp-finite":[5],"element":[6,35,77],"subspaces":[7],"$\\boldsymbol{\\mathsf{H}}(\\mathop{{\\rm":[9,12],"div}},\\Omega)$":[10],"and":[11,54],"rot}},\\Omega)$":[13],"on":[14,37,79],"a":[15,65],"polygonal":[16],"domain":[17],"$\\Omega$":[18],"using":[19],"Brezzi--Douglas--Fortin--Marini":[20],"(BDFM)":[21],"or":[22],"Raviart--Thomas":[23],"(RT)":[24],"elements.":[25],"Approximation":[26],"theoretic":[27],"results":[28,62],"are":[29,101],"derived":[30],"for":[31,46,87,103],"the":[32,55,68,74,88,91],"hp-version":[33,75],"finite":[34,76],"method":[36,78],"non-quasi-uniform":[38],"meshes":[39,82],"quadrilateral":[41],"elements":[42],"with":[43],"hanging":[44],"nodes":[45],"functions":[47],"belonging":[48],"to":[49],"weighted":[50],"Sobolev":[51],"spaces":[52,58],"${\\boldsymbol{\\mathsf{H}}}_{\\omega}^{s,\\ell}(\\Omega)$":[53],"countably":[56],"normed":[57],"$\\pmb{{\\cal":[59],"B}}_{w}^{\\ell}(\\Omega)$.":[60],"These":[61],"culminate":[63],"in":[64,108],"proof":[66],"characteristic":[69],"exponential":[70,98],"convergence":[71,99],"property":[72],"suitably":[80],"designed":[81],"under":[83],"similar":[84],"conditions":[85],"needed":[86],"analysis":[89],"${\\boldsymbol{\\mathsf{H}}}^{1}(\\Omega)$":[92],"case.":[93],"By":[94],"way":[95],"illustration,":[97],"rates":[100],"deduced":[102],"mixed":[104],"hp-approximation":[105],"flow":[107],"porous":[109],"media.":[110]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2001775732","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-04-20T19:57:31.960302","created_date":"2016-06-24"}