{"id":"https://openalex.org/W2079976810","doi":"https://doi.org/10.1090/s0025-5718-03-01508-4","title":"Analysis of a bilinear finite element for shallow shells. II: Consistency error","display_name":"Analysis of a bilinear finite element for shallow shells. II: Consistency error","publication_year":2003,"publication_date":"2003-03-04","ids":{"openalex":"https://openalex.org/W2079976810","doi":"https://doi.org/10.1090/s0025-5718-03-01508-4","mag":"2079976810"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-03-01508-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-03-01508-4","pdf_url":"https://www.ams.org/mcom/2003-72-244/S0025-5718-03-01508-4/S0025-5718-03-01508-4.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/2003-72-244/S0025-5718-03-01508-4/S0025-5718-03-01508-4.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":false,"raw_author_name":"Ville Havu","raw_affiliation_strings":["Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 Helsinki University of Technology, Finland","Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 Helsinki Univ. of Tech., Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 Helsinki University of Technology, Finland","institution_ids":[]},{"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 University of Technology, Finland","Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 Helsinki Univ. of Tech., Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 Helsinki University of Technology, Finland","institution_ids":[]},{"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":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I2800229700"],"apc_list":null,"apc_paid":null,"fwci":2.2371,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.87262841,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"72","issue":"244","first_page":"1635","last_page":"1653"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9995999932289124,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.9973000288009644,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7024742364883423},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7006866335868835},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.6116271018981934},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6061415076255798},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.5929094552993774},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5044718980789185},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5023040771484375},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4519035220146179},{"id":"https://openalex.org/keywords/shear","display_name":"Shear (geology)","score":0.41015511751174927},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16434717178344727},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.10028660297393799},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09712108969688416},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.09558987617492676}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7024742364883423},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7006866335868835},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.6116271018981934},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6061415076255798},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.5929094552993774},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5044718980789185},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5023040771484375},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4519035220146179},{"id":"https://openalex.org/C96035792","wikidata":"https://www.wikidata.org/wiki/Q43606218","display_name":"Shear (geology)","level":2,"score":0.41015511751174927},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16434717178344727},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.10028660297393799},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09712108969688416},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.09558987617492676},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-03-01508-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-03-01508-4","pdf_url":"https://www.ams.org/mcom/2003-72-244/S0025-5718-03-01508-4/S0025-5718-03-01508-4.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:10.1.1.668.5560","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.668.5560","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://lib.tkk.fi/Diss/2001/isbn9512256983/article3.pdf?origin%3Dpublication_detail","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-03-01508-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-03-01508-4","pdf_url":"https://www.ams.org/mcom/2003-72-244/S0025-5718-03-01508-4/S0025-5718-03-01508-4.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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1492326914","https://openalex.org/W1602485028","https://openalex.org/W1988235858","https://openalex.org/W2006545123","https://openalex.org/W2078548624","https://openalex.org/W2129971090","https://openalex.org/W2131130542","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W2165589608","https://openalex.org/W3093557575","https://openalex.org/W2354231916","https://openalex.org/W2162140574","https://openalex.org/W3182767856","https://openalex.org/W2354073393","https://openalex.org/W2361009070","https://openalex.org/W2378988399","https://openalex.org/W1983356840","https://openalex.org/W2121457398"],"abstract_inverted_index":{"We":[0,17,33],"consider":[1],"a":[2,12,174],"bilinear":[3],"reduced-strain":[4],"finite":[5,47],"element":[6,24,48],"of":[7,22,31,53,122,143,219],"the":[8,19,23,37,44,46,51,54,120,141,144,158,178,181,284,289],"MITC":[9],"family":[10],"for":[11],"shallow":[13],"Reissner-Naghdi":[14],"type":[15],"shell.":[16],"estimate":[18],"consistency":[20,286],"error":[21,57,287],"in":[25,36],"both":[26],"membrane-":[27],"and":[28,50,161,214],"bending-dominated":[29,179],"states":[30],"deformation.":[32],"prove":[34],"that":[35,212,279],"membrane-dominated":[38],"case,":[39,180],"under":[40,280],"severe":[41],"assumptions":[42,283],"on":[43],"domain,":[45],"mesh":[49,159],"regularity":[52,282],"solution,":[55],"an":[56],"bound":[58,184,290],"<inline-formula":[59,128,146,162,185,221,249,291],"content-type=\"math/mathml\">":[60,129,147,163,186,222,250,292],"<mml:math":[61,130,148,164,187,223,251,293],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[62,131,149,165,188,224,252,294],"alttext=\"upper":[63,189,225,295],"O":[64,190,226,296],"left-parenthesis":[65,191,227,297],"h":[66,73,192,298],"plus":[67,76],"t":[68,228],"Superscript":[69,74],"negative":[70],"1":[71,75],"Baseline":[72,78],"s":[77],"right-parenthesis\">":[79,193,230,299],"<mml:semantics>":[80,133,151,167,194,231,256,300],"<mml:mrow>":[81,195,232,257,301],"<mml:mi>O</mml:mi>":[82,196,233,302],"<mml:mo":[83,106,197,200,234,240,259,303,306],"stretchy=\"false\">(</mml:mo>":[84,198,235,304],"<mml:mi>h</mml:mi>":[85,98,152,199,305],"<mml:mo>+</mml:mo>":[86,102],"<mml:msup>":[87,97,236],"<mml:mi>t</mml:mi>":[88,134,237,258],"<mml:mrow":[89,99],"class=\"MJX-TeXAtom-ORD\">":[90,100],"<mml:mo>":[91],"\u2212":[92],"</mml:mo>":[93,262],"<mml:mn>1</mml:mn>":[94,101],"</mml:mrow>":[95,104,108,202,242,264,308],"</mml:msup>":[96,105,239],"<mml:mi>s</mml:mi>":[103,168],"stretchy=\"false\">)</mml:mo>":[107,201,241,307],"<mml:annotation":[109,135,153,169,203,243,265,309],"encoding=\"application/x-tex\">O(h":[110],"+":[111],"t^{-1}h^{1+s})</mml:annotation>":[112],"</mml:semantics>":[113,137,155,171,205,245,269,311],"</mml:math>":[114,138,156,172,206,246,270,312],"</inline-formula>":[115,139,157,173,207,247,271,313],"can":[116],"be":[117],"obtained":[118],"if":[119],"contribution":[121],"transverse":[123,215],"shear":[124,216],"is":[125,140,208],"neglected.":[126],"Here":[127],"alttext=\"t\">":[132],"encoding=\"application/x-tex\">t</mml:annotation>":[136],"thickness":[142],"shell,":[145],"alttext=\"h\">":[150],"encoding=\"application/x-tex\">h</mml:annotation>":[154],"spacing,":[160],"alttext=\"s\">":[166],"encoding=\"application/x-tex\">s</mml:annotation>":[170],"smoothness":[175],"parameter.":[176],"In":[177,273],"uniformly":[182],"optimal":[183],"encoding=\"application/x-tex\">O(h)</mml:annotation>":[204,310],"achievable":[209],"but":[210],"requires":[211],"membrane":[213],"strains":[217],"are":[218],"order":[220],"squared":[229],"<mml:mn>2</mml:mn>":[238],"encoding=\"application/x-tex\">O(t^2)</mml:annotation>":[244],"as":[248],"alttext=\"t":[253],"right-arrow":[254],"0\">":[255],"stretchy=\"false\">":[260],"\u2192":[261],"<mml:mn>0</mml:mn>":[263],"encoding=\"application/x-tex\">t":[266],"\\rightarrow":[267],"0</mml:annotation>":[268],".":[272,314],"this":[274],"case":[275],"we":[276],"also":[277],"show":[278],"sufficient":[281],"asymptotic":[285],"has":[288]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
