{"id":"https://openalex.org/W4403021610","doi":"https://doi.org/10.1515/cmam-2024-0060","title":"A <i>P</i> <sub>2</sub> H-Div-Nonconforming-H-Curl Finite Element for the Stokes Equations on Triangular Meshes","display_name":"A <i>P</i> <sub>2</sub> H-Div-Nonconforming-H-Curl Finite Element for the Stokes Equations on Triangular Meshes","publication_year":2024,"publication_date":"2024-10-01","ids":{"openalex":"https://openalex.org/W4403021610","doi":"https://doi.org/10.1515/cmam-2024-0060"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2024-0060","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2024-0060","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114049559","display_name":"Yunqing Huang","orcid":"https://orcid.org/0000-0002-0404-0638"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yunqing Huang","raw_affiliation_strings":["School of Mathematics and Computational Science , Xiangtan University , Xiangtan , Hunan 411105 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science , Xiangtan University , Xiangtan , Hunan 411105 , P. R. China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100742189","display_name":"Xuejun Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuejun Xu","raw_affiliation_strings":["School of Mathematical Science , Tongji University ; and Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Tongji University , Shanghai 200092 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Science , Tongji University ; and Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Tongji University , Shanghai 200092 , P. R. China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040152867","display_name":"Shangyou Zhang","orcid":"https://orcid.org/0000-0002-1114-4179"},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shangyou Zhang","raw_affiliation_strings":["Department of Mathematical Sciences , University of Delaware , Newark , DE 19716 , USA"],"raw_orcid":"https://orcid.org/0000-0002-1114-4179","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , University of Delaware , Newark , DE 19716 , USA","institution_ids":["https://openalex.org/I86501945"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5114049559"],"corresponding_institution_ids":["https://openalex.org/I4610292"],"apc_list":null,"apc_paid":null,"fwci":0.7166,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.66501272,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"25","issue":"2","first_page":"459","last_page":"473"},"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":0.9997000098228455,"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":0.9997000098228455,"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":0.9958000183105469,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9937999844551086,"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/curl","display_name":"Curl (programming language)","score":0.8563231229782104},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.8346689939498901},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7461180686950684},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5600526928901672},{"id":"https://openalex.org/keywords/stokes-problem","display_name":"Stokes problem","score":0.4696333408355713},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41675353050231934},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3456466794013977},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25773757696151733},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2505091726779938},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2091732621192932}],"concepts":[{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.8563231229782104},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.8346689939498901},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7461180686950684},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5600526928901672},{"id":"https://openalex.org/C2780355006","wikidata":"https://www.wikidata.org/wiki/Q30715867","display_name":"Stokes problem","level":3,"score":0.4696333408355713},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41675353050231934},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3456466794013977},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25773757696151733},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2505091726779938},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2091732621192932},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2024-0060","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2024-0060","pdf_url":null,"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":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2100893353","display_name":null,"funder_award_id":"12331015","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G629589318","display_name":null,"funder_award_id":"12071350","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G854124391","display_name":null,"funder_award_id":"11971410","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8858228672","display_name":null,"funder_award_id":"2020 YFA 0713500","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W209576205","https://openalex.org/W1973212083","https://openalex.org/W1980036878","https://openalex.org/W1994892733","https://openalex.org/W2005632248","https://openalex.org/W2007903663","https://openalex.org/W2009985306","https://openalex.org/W2014220840","https://openalex.org/W2015696101","https://openalex.org/W2058241749","https://openalex.org/W2092168430","https://openalex.org/W2098717681","https://openalex.org/W2113267855","https://openalex.org/W2118395915","https://openalex.org/W2119134040","https://openalex.org/W2157023312","https://openalex.org/W2474482124","https://openalex.org/W2729404336","https://openalex.org/W2962917950","https://openalex.org/W2998796568","https://openalex.org/W3011045723","https://openalex.org/W3156199883","https://openalex.org/W3160772952","https://openalex.org/W3163626107","https://openalex.org/W3184455434","https://openalex.org/W3199442144","https://openalex.org/W4386136612","https://openalex.org/W4389396068","https://openalex.org/W6600388300","https://openalex.org/W6614189368"],"related_works":["https://openalex.org/W2382844561","https://openalex.org/W2083529992","https://openalex.org/W816511862","https://openalex.org/W1557607869","https://openalex.org/W2238883956","https://openalex.org/W2376992165","https://openalex.org/W2784995402","https://openalex.org/W2056259617","https://openalex.org/W3016132316","https://openalex.org/W3174219354"],"abstract_inverted_index":{"Abstract":[0],"The":[1,24,68],"P2":[2],"BDM":[3],"H-div":[4,29],"finite":[5,26,38,118],"element":[6,27,39,52,106],"is":[7,31,55],"enriched":[8],"by":[9,74],"five":[10],"<m:math":[11,44,79,109],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[12,45,80,110],"<m:msub>":[13,46,81,111],"<m:mi>P</m:mi>":[14,47,82,112],"<m:mn>5</m:mn>":[15,83],"</m:msub>":[16,49,84,114],"</m:math>":[17,50,85,115],"P_{5}":[18,86],"divergence-free":[19,59,87,105],"bubbles":[20],"on":[21,65],"each":[22,89],"triangle.":[23],"resulting":[25],"remains":[28],"and":[30,57,95],"also":[32,71],"H-curl":[33],"nonconforming.":[34],"Thus":[35],"the":[36,42,62,101,104,108],"new":[37],"combined":[40],"with":[41],"discontinuous":[43],"<m:mn>1</m:mn>":[48],"P_{1}":[51],"for":[53],"pressure,":[54],"stabilizer-free":[56],"still":[58],"in":[60,93,96],"solving":[61],"Stokes":[63],"equations":[64],"triangular":[66],"meshes.":[67],"stabilization":[69],"can":[70],"be":[72],"done":[73],"three,":[75],"four,":[76],"or":[77],"six":[78],"bubble-enrichment":[88],"triangle,":[90],"shown":[91],"both":[92],"theory":[94],"computation.":[97],"Numerical":[98],"tests":[99],"show":[100],"advantage":[102],"of":[103],"over":[107],"<m:mn>2</m:mn>":[113],"P_{2}":[116],"Taylor\u2013Hood":[117],"element.":[119]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2025-12-21T01:58:51.020947","created_date":"2025-10-10T00:00:00"}