{"id":"https://openalex.org/W2006545123","doi":"https://doi.org/10.1090/s0025-5718-01-01376-x","title":"Analysis of a bilinear finite element for shallow shells I: Approximation of inextensional deformations","display_name":"Analysis of a bilinear finite element for shallow shells I: Approximation of inextensional deformations","publication_year":2001,"publication_date":"2001-11-20","ids":{"openalex":"https://openalex.org/W2006545123","doi":"https://doi.org/10.1090/s0025-5718-01-01376-x","mag":"2006545123"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01376-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01376-x","pdf_url":"https://www.ams.org/mcom/2002-71-239/S0025-5718-01-01376-X/S0025-5718-01-01376-X.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":null,"license_id":null,"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":"bronze","oa_url":"https://www.ams.org/mcom/2002-71-239/S0025-5718-01-01376-X/S0025-5718-01-01376-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086414326","display_name":"Ville Havu","orcid":null},"institutions":[{"id":"https://openalex.org/I2800229700","display_name":"Helsinki Institute of Physics","ror":"https://ror.org/01x2x1522","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I2800229700","https://openalex.org/I63548447","https://openalex.org/I94722563","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Ville Havu","raw_affiliation_strings":["Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 Helsinki Univ. of Tech., Finland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 Helsinki Univ. of Tech., Finland","institution_ids":["https://openalex.org/I2800229700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044231351","display_name":"Juhani Pitk\u00e4ranta","orcid":null},"institutions":[{"id":"https://openalex.org/I2800229700","display_name":"Helsinki Institute of Physics","ror":"https://ror.org/01x2x1522","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I2800229700","https://openalex.org/I63548447","https://openalex.org/I94722563","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Juhani Pitk\u00e4ranta","raw_affiliation_strings":["Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 Helsinki Univ. of Tech., Finland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 Helsinki Univ. of Tech., Finland","institution_ids":["https://openalex.org/I2800229700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086414326"],"corresponding_institution_ids":["https://openalex.org/I2800229700"],"apc_list":null,"apc_paid":null,"fwci":4.246,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.93150248,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"71","issue":"239","first_page":"923","last_page":"943"},"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":0.9991000294685364,"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":0.9973000288009644,"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":0.8332251906394958},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6825144290924072},{"id":"https://openalex.org/keywords/bilinear-form","display_name":"Bilinear form","score":0.623236894607544},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5969640016555786},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5901477932929993},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.568707287311554},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5342622995376587},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.5133177638053894},{"id":"https://openalex.org/keywords/partition-of-unity","display_name":"Partition of unity","score":0.48599061369895935},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.46459102630615234},{"id":"https://openalex.org/keywords/displacement-field","display_name":"Displacement field","score":0.41271182894706726}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8332251906394958},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6825144290924072},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.623236894607544},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5969640016555786},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5901477932929993},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.568707287311554},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5342622995376587},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.5133177638053894},{"id":"https://openalex.org/C102205669","wikidata":"https://www.wikidata.org/wiki/Q191690","display_name":"Partition of unity","level":3,"score":0.48599061369895935},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.46459102630615234},{"id":"https://openalex.org/C29660869","wikidata":"https://www.wikidata.org/wiki/Q5282615","display_name":"Displacement field","level":3,"score":0.41271182894706726},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/s0025-5718-01-01376-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01376-x","pdf_url":"https://www.ams.org/mcom/2002-71-239/S0025-5718-01-01376-X/S0025-5718-01-01376-X.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.187.5404","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.187.5404","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/2003-72-244/S0025-5718-03-01508-4/S0025-5718-03-01508-4.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.7456","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.7456","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/2002-71-239/S0025-5718-01-01376-X/S0025-5718-01-01376-X.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.99.1408","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.99.1408","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/mcom/2002-71-239/S0025-5718-01-01376-X/S0025-5718-01-01376-X.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.99.9635","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.99.9635","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/mcom/2003-72-244/S0025-5718-03-01508-4/S0025-5718-03-01508-4.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01376-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01376-x","pdf_url":"https://www.ams.org/mcom/2002-71-239/S0025-5718-01-01376-X/S0025-5718-01-01376-X.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":null,"license_id":null,"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","score":0.6000000238418579,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2006545123.pdf","grobid_xml":"https://content.openalex.org/works/W2006545123.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1598463102","https://openalex.org/W1602485028","https://openalex.org/W2049917851","https://openalex.org/W2049996170","https://openalex.org/W2059174743","https://openalex.org/W2059694388","https://openalex.org/W2078548624","https://openalex.org/W2090329921","https://openalex.org/W2129971090","https://openalex.org/W2131130542","https://openalex.org/W4233463143"],"related_works":["https://openalex.org/W4200053212","https://openalex.org/W4249269526","https://openalex.org/W2235548299","https://openalex.org/W2558547733","https://openalex.org/W4220877270","https://openalex.org/W1963546854","https://openalex.org/W4229676496","https://openalex.org/W2197675418","https://openalex.org/W2357064270","https://openalex.org/W1976845455"],"abstract_inverted_index":{"We":[0,29,42,74],"consider":[1],"a":[2,9],"bilinear":[3],"reduced-strain":[4],"finite":[5,52],"element":[6,53],"formulation":[7,17],"for":[8,78,124],"shallow":[10],"shell":[11,98,104],"model":[12],"of":[13,33,70,90,102],"Reissner\u2013Naghdi":[14],"type.":[15],"The":[16,138],"is":[18,89,109,121,141],"closely":[19],"related":[20],"to":[21,96,143],"the":[22,31,44,48,51,59,65,71,82,86,97,106,125,129,135],"facet":[23],"models":[24],"used":[25],"in":[26,68,85,113],"engineering":[27],"practice.":[28],"estimate":[30],"error":[32,107,139],"this":[34],"scheme":[35],"when":[36],"approximating":[37],"an":[38],"inextensional":[39],"displacement":[40],"field.":[41],"make":[43],"strong":[45],"assumptions":[46],"that":[47,58,77],"domain":[49],"and":[50,57,64,115],"mesh":[54,66,136],"are":[55,62,132],"rectangular":[56],"boundary":[60],"conditions":[61],"periodic":[63],"uniform":[67],"one":[69],"coordinate":[72],"directions.":[73],"prove":[75],"then":[76],"sufficiently":[79],"smooth":[80],"fields,":[81],"convergence":[83],"rate":[84],"energy":[87],"norm":[88],"optimal":[91],"order":[92],"uniformly":[93],"with":[94,134],"respect":[95],"thickness.":[99],"In":[100],"case":[101],"elliptic":[103],"geometry":[105],"bound":[108,140],"furthermore":[110],"quasioptimal,":[111],"whereas":[112],"parabolic":[114],"hyperbolic":[116],"geometries":[117],"slightly":[118],"enhanced":[119],"smoothness":[120],"required,":[122],"except":[123],"degenerate":[126],"cases":[127],"where":[128],"characteristic":[130],"lines":[131],"parallel":[133],"lines.":[137],"shown":[142],"be":[144],"sharp.":[145]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}