{"id":"https://openalex.org/W2125482314","doi":"https://doi.org/10.1155/2012/156095","title":"Superconvergence Analysis of Finite Element Method for a Second\u2010Type Variational Inequality","display_name":"Superconvergence Analysis of Finite Element Method for a Second\u2010Type Variational Inequality","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2125482314","doi":"https://doi.org/10.1155/2012/156095","mag":"2125482314"},"language":"en","primary_location":{"id":"doi:10.1155/2012/156095","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/156095","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/156095.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/156095.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019184470","display_name":"Dongyang Shi","orcid":"https://orcid.org/0000-0003-3945-6796"},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongyang Shi","raw_affiliation_strings":["Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China","Department of Mathematics, Zhengzhou University, Zhengzhou 450001"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China","institution_ids":["https://openalex.org/I38877650"]},{"raw_affiliation_string":"Department of Mathematics, Zhengzhou University, Zhengzhou 450001","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102838030","display_name":"Hongbo Guan","orcid":"https://orcid.org/0000-0002-0160-7889"},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]},{"id":"https://openalex.org/I23171815","display_name":"Zhengzhou University of Light Industry","ror":"https://ror.org/05fwr8z16","country_code":"CN","type":"education","lineage":["https://openalex.org/I23171815"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongbo Guan","raw_affiliation_strings":["Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, China","Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China","Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002","Department of Mathematics, Zhengzhou University, Zhengzhou 450001"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, China","institution_ids":["https://openalex.org/I23171815"]},{"raw_affiliation_string":"Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China","institution_ids":["https://openalex.org/I38877650"]},{"raw_affiliation_string":"Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002","institution_ids":["https://openalex.org/I23171815"]},{"raw_affiliation_string":"Department of Mathematics, Zhengzhou University, Zhengzhou 450001","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065954569","display_name":"Xiaofei Guan","orcid":"https://orcid.org/0000-0002-2062-2486"},"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":true,"raw_author_name":"Xiaofei Guan","raw_affiliation_strings":["Department of Mathematics, Tongji University, Shanghai 200092, China","Department of Mathematics, Tongji University, Shanghai 200092"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tongji University, Shanghai 200092, China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"Department of Mathematics, Tongji University, Shanghai 200092","institution_ids":["https://openalex.org/I116953780"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065954569"],"corresponding_institution_ids":["https://openalex.org/I116953780"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.3493,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.64682801,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"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/T10514","display_name":"Numerical methods in engineering","score":0.9991999864578247,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9983000159263611,"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/algorithm","display_name":"Algorithm","score":0.6026940941810608},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3515138626098633},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32095205783843994}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6026940941810608},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3515138626098633},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32095205783843994}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/156095","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/156095","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/156095.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1357153594","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1357153594","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:156095","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/156095.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:d00dd3b1131d4aa3ba340ae9ec470072","is_oa":true,"landing_page_url":"https://doaj.org/article/d00dd3b1131d4aa3ba340ae9ec470072","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/156095","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/156095","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/156095.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5699999928474426,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5262524592","display_name":null,"funder_award_id":"11126132","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7284392917","display_name":null,"funder_award_id":"10971203","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2125482314.pdf","grobid_xml":"https://content.openalex.org/works/W2125482314.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W798080335","https://openalex.org/W1031327728","https://openalex.org/W1513782764","https://openalex.org/W1963795254","https://openalex.org/W1998544309","https://openalex.org/W2009371127","https://openalex.org/W2032620133","https://openalex.org/W2033105470","https://openalex.org/W2041983444","https://openalex.org/W2061584371","https://openalex.org/W2074987839","https://openalex.org/W2095457037","https://openalex.org/W2116579948","https://openalex.org/W2254273306","https://openalex.org/W2361869628","https://openalex.org/W2376836354","https://openalex.org/W2494779131","https://openalex.org/W2616717838","https://openalex.org/W2721539309","https://openalex.org/W4234028290","https://openalex.org/W4242517046","https://openalex.org/W4292166829","https://openalex.org/W6998535792","https://openalex.org/W7057401489"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W2350741829"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,36,51,77],"finite":[4],"element":[5],"(FE)":[6],"approximation":[7],"to":[8,46,75],"a":[9,32],"second\u2010type":[10],"variational":[11],"inequality.":[12],"The":[13,54],"supe":[14],"rclose":[15],"and":[16,25],"superconvergence":[17],"results":[18,72],"are":[19,73],"obtained":[20],"for":[21,64],"conforming":[22],"bilinear":[23],"FE":[24,29],"nonconforming":[26],"EQ":[27,65],"rot":[28,66],"schemes":[30],"under":[31],"reasonable":[33],"regularity":[34],"of":[35],"exact":[37],"solution":[38],"u":[39],"\u2208":[40],"H":[41],"5/2":[42],"(\u03a9),":[43],"which":[44],"seem":[45],"be":[47],"never":[48],"discovered":[49],"in":[50],"previous":[52],"literature.":[53],"optimal":[55],"L":[56],"2":[57],"\u2010norm":[58],"error":[59],"estimate":[60],"is":[61],"also":[62],"derived":[63],"FE.":[67],"At":[68],"last,":[69],"some":[70],"numerical":[71],"provided":[74],"verify":[76],"theoretical":[78],"analysis.":[79]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2016-06-24T00:00:00"}