{"id":"https://openalex.org/W1981807311","doi":"https://doi.org/10.1137/s003614290239590x","title":"Conditioning of Hierarchic <i>p</i>-Version N\u00e9d\u00e9lec Elements on Meshes of Curvilinear Quadrilaterals and Hexahedra","display_name":"Conditioning of Hierarchic <i>p</i>-Version N\u00e9d\u00e9lec Elements on Meshes of Curvilinear Quadrilaterals and Hexahedra","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1981807311","doi":"https://doi.org/10.1137/s003614290239590x","mag":"1981807311"},"language":"fr","primary_location":{"id":"doi:10.1137/s003614290239590x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614290239590x","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/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"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108472690","display_name":"Joe Coyle","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joe Coyle","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.9216,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.94763227,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"41","issue":"2","first_page":"731","last_page":"750"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9988999962806702,"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/curvilinear-coordinates","display_name":"Curvilinear coordinates","score":0.9276734590530396},{"id":"https://openalex.org/keywords/curl","display_name":"Curl (programming language)","score":0.8598792552947998},{"id":"https://openalex.org/keywords/quadrilateral","display_name":"Quadrilateral","score":0.7782624959945679},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7297829389572144},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.6020697951316833},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5962230563163757},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5659372210502625},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5226256847381592},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.476835161447525},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4444173574447632},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37627121806144714},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.34625372290611267},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1639908254146576},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11084595322608948},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09365522861480713}],"concepts":[{"id":"https://openalex.org/C98343798","wikidata":"https://www.wikidata.org/wiki/Q1790208","display_name":"Curvilinear coordinates","level":2,"score":0.9276734590530396},{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.8598792552947998},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.7782624959945679},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7297829389572144},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.6020697951316833},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5962230563163757},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5659372210502625},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5226256847381592},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.476835161447525},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4444173574447632},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37627121806144714},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.34625372290611267},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1639908254146576},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11084595322608948},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09365522861480713},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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":1,"locations":[{"id":"doi:10.1137/s003614290239590x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614290239590x","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6800000071525574,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1488435683","https://openalex.org/W1605773447","https://openalex.org/W1993946089","https://openalex.org/W2007233211","https://openalex.org/W2030327292","https://openalex.org/W2061253771","https://openalex.org/W2062618977","https://openalex.org/W2062969160","https://openalex.org/W2066450870","https://openalex.org/W2067621714","https://openalex.org/W2072247902","https://openalex.org/W2074250763","https://openalex.org/W2112733149","https://openalex.org/W2115657303","https://openalex.org/W2152189126","https://openalex.org/W2156779443","https://openalex.org/W2325830745","https://openalex.org/W2610857016","https://openalex.org/W2731873610"],"related_works":["https://openalex.org/W1133267572","https://openalex.org/W2403317455","https://openalex.org/W3035933954","https://openalex.org/W2005478455","https://openalex.org/W2368295716","https://openalex.org/W3135949361","https://openalex.org/W1968086293","https://openalex.org/W3201757880","https://openalex.org/W2090955020","https://openalex.org/W2376658924"],"abstract_inverted_index":{"The":[0,54],"conditioning":[1],"of":[2,5,14,27,34,51,60,79,106],"a":[3],"set":[4],"hierarchic":[6],"basis":[7],"functions":[8],"for":[9,38],"p-version":[10],"edge":[11],"element":[12],"approximation":[13,50,80],"the":[15,25,28,32,35,39,72,76,84,94,104],"space":[16],"H(curl)":[17],"is":[18,56,81,86],"studied.":[19],"Theoretical":[20],"bounds":[21,97],"are":[22,98,101],"obtained":[23],"on":[24,31],"location":[26],"eigenvalues":[29],"and":[30,42,67,100],"growth":[33],"condition":[36],"numbers":[37],"mass,":[40],"curl-curl,":[41],"stiffness":[43],"matrices":[44],"that":[45,91,93],"naturally":[46],"arise":[47],"from":[48],"Galerkin":[49],"Maxwell's":[52],"equations.":[53],"theory":[55,85],"applicable":[57],"to":[58],"meshes":[59],"curvilinear":[61],"quadrilaterals":[62],"or":[63],"hexahedra":[64],"in":[65,74],"two":[66],"three":[68],"dimensions,":[69],"respectively,":[70],"including":[71],"case":[73],"which":[75],"local":[77],"order":[78],"nonuniform.":[82],"Throughout,":[83],"illustrated":[87],"with":[88],"numerical":[89],"examples":[90],"show":[92],"theoretical":[95],"asymptotic":[96],"sharp":[99],"attained":[102],"within":[103],"range":[105],"practical":[107],"computation.":[108]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
