{"id":"https://openalex.org/W4210487040","doi":"https://doi.org/10.1137/21m1391006","title":"A $C^1$ Conforming Petrov--Galerkin Method for Convection-Diffusion Equations and Superconvergence Analysis over Rectangular Meshes","display_name":"A $C^1$ Conforming Petrov--Galerkin Method for Convection-Diffusion Equations and Superconvergence Analysis over Rectangular Meshes","publication_year":2022,"publication_date":"2022-02-01","ids":{"openalex":"https://openalex.org/W4210487040","doi":"https://doi.org/10.1137/21m1391006"},"language":"en","primary_location":{"id":"doi:10.1137/21m1391006","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1391006","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/A5021695845","display_name":"Waixiang Cao","orcid":"https://orcid.org/0000-0003-2434-7300"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Waixiang Cao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112046430","display_name":"Lueling Jia","orcid":"https://orcid.org/0009-0001-9662-4875"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lueling Jia","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100406520","display_name":"Zhimin Zhang","orcid":"https://orcid.org/0000-0002-0531-9112"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhimin Zhang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021695845"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6645,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.59630327,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"60","issue":"1","first_page":"274","last_page":"311"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.9743180274963379},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8635891079902649},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.731339693069458},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.567950427532196},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.5625482797622681},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5048978924751282},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5007045269012451},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.49770691990852356},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4881754517555237},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4676479995250702},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4308880865573883},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3486165702342987}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9743180274963379},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8635891079902649},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.731339693069458},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.567950427532196},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.5625482797622681},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5048978924751282},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5007045269012451},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.49770691990852356},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4881754517555237},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4676479995250702},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4308880865573883},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3486165702342987},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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:10.1137/21m1391006","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1391006","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":[],"awards":[{"id":"https://openalex.org/G1697073492","display_name":null,"funder_award_id":"11871106","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1872226553","display_name":null,"funder_award_id":"U1930402","funder_id":"https://openalex.org/F4320335578","funder_display_name":"NSAF Joint Fund"},{"id":"https://openalex.org/G4646362747","display_name":null,"funder_award_id":"11871092","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation 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/F4320335578","display_name":"NSAF Joint Fund","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W118329571","https://openalex.org/W1873489324","https://openalex.org/W1971723751","https://openalex.org/W1976385614","https://openalex.org/W1981510480","https://openalex.org/W1984320368","https://openalex.org/W1986550841","https://openalex.org/W2001012793","https://openalex.org/W2003444950","https://openalex.org/W2005601391","https://openalex.org/W2010194973","https://openalex.org/W2016419036","https://openalex.org/W2019098734","https://openalex.org/W2019415831","https://openalex.org/W2022591932","https://openalex.org/W2023025416","https://openalex.org/W2029214106","https://openalex.org/W2033255950","https://openalex.org/W2039277388","https://openalex.org/W2040299291","https://openalex.org/W2044190355","https://openalex.org/W2045662757","https://openalex.org/W2049351608","https://openalex.org/W2064682864","https://openalex.org/W2066090268","https://openalex.org/W2073897969","https://openalex.org/W2075388329","https://openalex.org/W2086298877","https://openalex.org/W2088288520","https://openalex.org/W2093156044","https://openalex.org/W2097739195","https://openalex.org/W2122074662","https://openalex.org/W2124227193","https://openalex.org/W2129283513","https://openalex.org/W2260148615","https://openalex.org/W2415686515","https://openalex.org/W2794861262","https://openalex.org/W2802944367"],"related_works":["https://openalex.org/W2019032602","https://openalex.org/W3199641408","https://openalex.org/W2597229022","https://openalex.org/W2947552135","https://openalex.org/W2014920306","https://openalex.org/W2984453791","https://openalex.org/W1982175859","https://openalex.org/W2788781272","https://openalex.org/W2474544633","https://openalex.org/W2069036386"],"abstract_inverted_index":{"In":[0,74,119],"this":[1],"paper,":[2],"a":[3,22,76,107,128],"new":[4,85],"$C^1$-conforming":[5,23],"Petrov--Galerkin":[6],"method":[7,20,86],"for":[8,98],"convection-diffusion":[9],"equations":[10],"is":[11,21,43,61],"designed":[12],"and":[13,55,63,87,102,111,116],"analyzed.":[14],"The":[15],"trial":[16],"space":[17,38,42],"of":[18,29,31,57,83,106],"our":[19],"${\\mathbb":[24,50],"Q}_k$":[25],"(i.e.,":[26],"tensor":[27],"product":[28],"polynomials":[30],"degree":[32],"at":[33,92,104,112],"most":[34],"$k$)":[35],"finite":[36],"element":[37],"while":[39],"the":[40,46,58,68,84,113,123,133,145],"test":[41],"taken":[44],"as":[45],"$L^2$":[47],"(discontinuous)":[48],"piecewise":[49],"Q}_{k-2}$":[51],"polynomial":[52],"space.":[53],"Existence":[54],"uniqueness":[56],"numerical":[59],"solution":[60],"proved":[62],"optimal":[64],"error":[65,130],"estimates":[66,131],"in":[67,132],"$L^2$-,":[69,134],"$H^1$-,":[70,135],"$H^2$-norms":[71,136],"are":[72,90,137,141],"proved.":[73],"addition,":[75],"rigorous":[77],"theoretical":[78,146],"analysis":[79],"establishes":[80],"superconvergence":[81,88],"properties":[82],"points/lines":[89],"identified":[91],"mesh":[93],"nodes":[94],"(with":[95],"order":[96,120],"$2k-2$":[97],"both":[99],"function":[100],"value":[101],"derivatives),":[103],"roots":[105],"special":[108],"Jacobi":[109],"polynomial,":[110],"Lobatto":[114],"lines":[115],"Gauss":[117],"lines.":[118],"to":[121,143],"reduce":[122],"global":[124],"regularity":[125],"requirement,":[126],"interior":[127],"priori":[129],"derived.":[138],"Numerical":[139],"experiments":[140],"presented":[142],"confirm":[144],"findings.":[147]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
