{"id":"https://openalex.org/W2084506701","doi":"https://doi.org/10.1090/s0025-5718-07-01952-7","title":"Two lower order nonconforming rectangular elements for the Reissner-Mindlin plate","display_name":"Two lower order nonconforming rectangular elements for the Reissner-Mindlin plate","publication_year":2007,"publication_date":"2007-07-26","ids":{"openalex":"https://openalex.org/W2084506701","doi":"https://doi.org/10.1090/s0025-5718-07-01952-7","mag":"2084506701"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-07-01952-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01952-7","pdf_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01952-7/S0025-5718-07-01952-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01952-7/S0025-5718-07-01952-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jun Hu","raw_affiliation_strings":["LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China","No 55, Zhong-Guan-Cun Dong Lu, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China"],"affiliations":[{"raw_affiliation_string":"LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"No 55, Zhong-Guan-Cun Dong Lu, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102146720","display_name":"Zhong\u2010Ci Shi","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhong-Ci Shi","raw_affiliation_strings":["No 55, Zhong-Guan-Cun Dong Lu, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China"],"affiliations":[{"raw_affiliation_string":"No 55, Zhong-Guan-Cun Dong Lu, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China","institution_ids":["https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028500115"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I20231570"],"apc_list":null,"apc_paid":null,"fwci":2.9993,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.90607683,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"76","issue":"260","first_page":"1771","last_page":"1787"},"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/T11366","display_name":"Elasticity and Material Modeling","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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":0.9991999864578247,"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/mathematics","display_name":"Mathematics","score":0.8731623888015747},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.6616227626800537},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.6490248441696167},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.5948799252510071},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.5902231931686401},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5254834294319153},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4931923747062683},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.42774662375450134},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4226984977722168},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41333815455436707},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11793464422225952}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8731623888015747},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.6616227626800537},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.6490248441696167},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5948799252510071},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.5902231931686401},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5254834294319153},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4931923747062683},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.42774662375450134},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4226984977722168},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41333815455436707},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11793464422225952},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-07-01952-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01952-7","pdf_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01952-7/S0025-5718-07-01952-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.4953","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.4953","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2007-76-260/S0025-5718-07-01952-7/S0025-5718-07-01952-7.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-07-01952-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01952-7","pdf_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01952-7/S0025-5718-07-01952-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.49000000953674316}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2084506701.pdf","grobid_xml":"https://content.openalex.org/works/W2084506701.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W915725826","https://openalex.org/W1492326914","https://openalex.org/W1500265572","https://openalex.org/W1536407545","https://openalex.org/W1852082788","https://openalex.org/W1966513386","https://openalex.org/W1969462451","https://openalex.org/W1970346369","https://openalex.org/W1970991388","https://openalex.org/W1976773674","https://openalex.org/W1979771104","https://openalex.org/W1986097487","https://openalex.org/W1995620712","https://openalex.org/W2007187208","https://openalex.org/W2009985306","https://openalex.org/W2035654636","https://openalex.org/W2040510504","https://openalex.org/W2041523977","https://openalex.org/W2069902256","https://openalex.org/W2072288941","https://openalex.org/W2088046906","https://openalex.org/W2092973465","https://openalex.org/W2129161483","https://openalex.org/W2130350269","https://openalex.org/W2147446841","https://openalex.org/W2166217386","https://openalex.org/W2415509676","https://openalex.org/W2569670394","https://openalex.org/W3149667697","https://openalex.org/W4244542537","https://openalex.org/W4245007249","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W2165589608","https://openalex.org/W3093557575","https://openalex.org/W3182767856","https://openalex.org/W2354231916","https://openalex.org/W2162140574","https://openalex.org/W2354073393","https://openalex.org/W2361009070","https://openalex.org/W2378988399","https://openalex.org/W2135183583","https://openalex.org/W2899165268"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"two":[5],"lower":[6],"order":[7],"nonconforming":[8,33,48],"rectangular":[9],"elements":[10,61],"for":[11],"the":[12,19,28,31,39,42,46,55,58,68,83,89],"Reissner-Mindlin":[13],"plate.":[14],"The":[15],"first":[16],"one":[17,44],"uses":[18,45],"conforming":[20],"bilinear":[21],"element":[22,36,51],"to":[23,37,52,66],"approximate":[24,38,53],"both":[25,54,75,88],"components":[26],"of":[27],"rotation,":[29],"and":[30,57,91,93],"modified":[32,47],"rotated":[34,49],"$Q_{1}$":[35,50],"displacement,":[40],"whereas":[41],"second":[43],"rotation":[56],"displacement.":[59],"Both":[60],"employ":[62],"a":[63],"projection":[64],"operator":[65],"overcome":[67],"shear":[69],"force":[70],"locking.":[71],"We":[72],"prove":[73],"that":[74],"methods":[76],"converge":[77],"at":[78],"optimal":[79],"rates":[80],"uniformly":[81],"in":[82,87],"plate":[84],"thickness":[85],"$t$":[86],"$H^{1}$-":[90],"$L^2$-norms,":[92],"consequently":[94],"they":[95],"are":[96],"locking":[97],"free.":[98]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
