{"id":"https://openalex.org/W3171979273","doi":"https://doi.org/10.1515/cmam-2021-0083","title":"Hierarchical Argyris Finite Element Method for Adaptive and Multigrid Algorithms","display_name":"Hierarchical Argyris Finite Element Method for Adaptive and Multigrid Algorithms","publication_year":2021,"publication_date":"2021-06-01","ids":{"openalex":"https://openalex.org/W3171979273","doi":"https://doi.org/10.1515/cmam-2021-0083","mag":"3171979273"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2021-0083","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2021-0083","pdf_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2021-0083/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"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":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2021-0083/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036808184","display_name":"Carsten Carstensen","orcid":null},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Carsten Carstensen","raw_affiliation_strings":["Humboldt-Universit\u00e4t zu Berlin , 10099 Berlin , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Humboldt-Universit\u00e4t zu Berlin , 10099 Berlin , Germany","institution_ids":["https://openalex.org/I39343248"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028500115","display_name":"Jun Hu","orcid":"https://orcid.org/0000-0002-4565-3000"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Hu","raw_affiliation_strings":["LMAM and School of Mathematical Sciences , Peking University , Beijing 100871 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMAM and School of Mathematical Sciences , Peking University , Beijing 100871 , P. R. China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036808184"],"corresponding_institution_ids":["https://openalex.org/I39343248"],"apc_list":null,"apc_paid":null,"fwci":1.2462,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.75988137,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"21","issue":"3","first_page":"529","last_page":"556"},"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":0.9958000183105469,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9927999973297119,"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/combinatorics","display_name":"Combinatorics","score":0.5341714024543762},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.49525681138038635},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3951346278190613},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.37773388624191284},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3425137400627136}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5341714024543762},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.49525681138038635},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3951346278190613},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37773388624191284},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3425137400627136},{"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:10.1515/cmam-2021-0083","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2021-0083","pdf_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2021-0083/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"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":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1515/cmam-2021-0083","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2021-0083","pdf_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2021-0083/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"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":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.4399999976158142,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1818906019","display_name":"Grundlagen und Anwendungen verallgemeinerter gemischter FEM f\u00fcr nichtlineare Probleme in der Festk\u00f6rpermechanik","funder_award_id":"255510958","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3761171619","display_name":null,"funder_award_id":"Project-ID 255510958 \u2013 SPP 1748","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5992293270","display_name":null,"funder_award_id":"SPP 1748","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G873693170","display_name":null,"funder_award_id":"11625101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320326177","display_name":"Chinesisch-Deutsche Zentrum f\u00fcr Wissenschaftsf\u00f6rderung","ror":"https://ror.org/03ny8r668"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3171979273.pdf","grobid_xml":"https://content.openalex.org/works/W3171979273.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W184031850","https://openalex.org/W184188664","https://openalex.org/W592368443","https://openalex.org/W628726389","https://openalex.org/W1530115438","https://openalex.org/W1548892666","https://openalex.org/W1592589766","https://openalex.org/W1975039968","https://openalex.org/W2000675710","https://openalex.org/W2014077116","https://openalex.org/W2017366188","https://openalex.org/W2024753911","https://openalex.org/W2027733726","https://openalex.org/W2040512322","https://openalex.org/W2044959876","https://openalex.org/W2048407683","https://openalex.org/W2056470693","https://openalex.org/W2071036364","https://openalex.org/W2084743165","https://openalex.org/W2092037996","https://openalex.org/W2107813568","https://openalex.org/W2111438170","https://openalex.org/W2129977146","https://openalex.org/W2199169705","https://openalex.org/W2765080741","https://openalex.org/W2769788317","https://openalex.org/W2963017886","https://openalex.org/W3204708751","https://openalex.org/W4210300254","https://openalex.org/W4211056248"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W2271181815"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"global":[2,31],"arrangement":[3],"of":[4,7,75,81,141,208],"the":[5,44,57,73,79,89,142,173],"degrees":[6],"freedom":[8],"in":[9,46,77],"a":[10,116,125,139],"standard":[11,90,143],"Argyris":[12,58,91,144],"finite":[13,59,92,145],"element":[14,60,93,146],"method":[15],"(FEM)":[16],"enforces":[17],"<m:math":[18,32,47,64,95,118,127,148,176,192,209,232],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[19,33,48,65,96,119,128,149,177,193,210,233],"<m:msup>":[20,34,49,66,98,151,212],"<m:mi>C</m:mi>":[21,35,67],"<m:mn>2</m:mn>":[22,51,68],"</m:msup>":[23,37,52,69,101,154,215],"</m:math>":[24,38,53,70,112,122,135,169,184,206,226],"{C^{2}}":[25,71],"at":[26,72],"interior":[27],"vertices,":[28],"while":[29],"solely":[30],"<m:mn>1</m:mn>":[36],"{C^{1}}":[39],"continuity":[40],"is":[41,137],"required":[42],"for":[43,84,230],"conformity":[45],"<m:mi>H</m:mi>":[50],"{H^{2}}":[54],".":[55,186],"Since":[56],"functions":[61],"are":[62],"not":[63,138],"midpoints":[74],"edges":[76],"general,":[78],"bisection":[80],"an":[82,190],"edge":[83],"mesh-refinement":[85],"leads":[86],"to":[87,115,172],"non-nestedness:":[88],"space":[94,147],"<m:mrow>":[97,103,150,156,194,197,211,217,234,235],"<m:mi>A</m:mi>":[99,152,195,213,236],"<m:mo>\u2032</m:mo>":[100,153,214],"<m:mo>\u2062</m:mo>":[102,155,196,216],"<m:mo":[104,108,157,165,198,202,218,222],"stretchy=\"false\">(</m:mo>":[105,158,199,219],"<m:mi":[106,120,131,161,180,200,220],"mathvariant=\"script\">\ud835\udcaf</m:mi>":[107,121,132,162,181,201,221],"stretchy=\"false\">)</m:mo>":[109,166,203,223],"</m:mrow>":[110,111,167,168,204,205,224,225],"{A^{\\prime}(\\mathcal{T})}":[113,227],"associated":[114,171],"triangulation":[117,175],"{\\mathcal{T}}":[123],"with":[124],"refinement":[126],"<m:mover":[129,159,178],"accent=\"true\">":[130,160,179],"<m:mo>^</m:mo>":[133,163,182],"</m:mover>":[134,164,183],"{\\widehat{\\mathcal{T}}}":[136,185],"subspace":[140],"{A^{\\prime}(\\widehat{\\mathcal{T}})}":[170],"refined":[174],"This":[187],"paper":[188],"suggests":[189],"extension":[191],"{A(\\mathcal{T})}":[207],"that":[228],"allows":[229],"nestedness":[231]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
