{"id":"https://openalex.org/W2008004031","doi":"https://doi.org/10.1137/s0036142902418357","title":"Least-Squares Methods for Linear Elasticity","display_name":"Least-Squares Methods for Linear Elasticity","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2008004031","doi":"https://doi.org/10.1137/s0036142902418357","mag":"2008004031"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142902418357","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902418357","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/A5023481731","display_name":"Zhiqiang Cai","orcid":"https://orcid.org/0000-0002-3775-7248"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhiqiang Cai","raw_affiliation_strings":["Purdue University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Purdue University","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066679330","display_name":"Gerhard Starke","orcid":"https://orcid.org/0000-0001-5985-173X"},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gerhard Starke","raw_affiliation_strings":["Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Hannover, Welfengarten 1, 30167 Hannover, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Hannover, Welfengarten 1, 30167 Hannover, Germany","institution_ids":["https://openalex.org/I114112103"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.8287,"has_fulltext":false,"cited_by_count":121,"citation_normalized_percentile":{"value":0.96986909,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"42","issue":"2","first_page":"826","last_page":"842"},"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":0.9994999766349792,"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":0.998199999332428,"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":0.8612291812896729},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6193943619728088},{"id":"https://openalex.org/keywords/linear-elasticity","display_name":"Linear elasticity","score":0.577637791633606},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5612220764160156},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5463762879371643},{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.4564724862575531},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.44157707691192627},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4356454610824585},{"id":"https://openalex.org/keywords/cauchy-stress-tensor","display_name":"Cauchy stress tensor","score":0.42750245332717896},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.42518097162246704},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23219674825668335}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8612291812896729},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6193943619728088},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.577637791633606},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5612220764160156},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5463762879371643},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.4564724862575531},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.44157707691192627},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4356454610824585},{"id":"https://openalex.org/C171338203","wikidata":"https://www.wikidata.org/wiki/Q13409892","display_name":"Cauchy stress tensor","level":2,"score":0.42750245332717896},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.42518097162246704},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23219674825668335},{"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},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036142902418357","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902418357","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.594.8385","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.594.8385","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.purdue.edu/~zcai/pdf-paper/04CaSt.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.7.6834","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.6834","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ifam.uni-hannover.de/~starke/papers/sdnew.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1250371188","display_name":"U.S.-Germany Cooperative Research:  Least-Square Finite Element Methods for Nonlinear Elasticity","funder_award_id":"9910010","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2817971656","display_name":"U.S.-Korea Cooperative Research Program:   Numerical methods for the computation of singular solutions and stress intensity factors","funder_award_id":"0139053","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W62043397","https://openalex.org/W136185420","https://openalex.org/W1492326914","https://openalex.org/W1674659126","https://openalex.org/W1852082788","https://openalex.org/W1965034652","https://openalex.org/W1981407574","https://openalex.org/W1985506636","https://openalex.org/W2006617763","https://openalex.org/W2006895912","https://openalex.org/W2014744421","https://openalex.org/W2041523977","https://openalex.org/W2048372739","https://openalex.org/W2073123170","https://openalex.org/W2075887353","https://openalex.org/W2075896209","https://openalex.org/W2079318234","https://openalex.org/W2093969996","https://openalex.org/W2099656682","https://openalex.org/W2101712703","https://openalex.org/W2105816608","https://openalex.org/W2127981460","https://openalex.org/W2489432230","https://openalex.org/W3149667697","https://openalex.org/W4205634890"],"related_works":["https://openalex.org/W3093564240","https://openalex.org/W2022688149","https://openalex.org/W2090301400","https://openalex.org/W2037320845","https://openalex.org/W1477078014","https://openalex.org/W4244084805","https://openalex.org/W2130874209","https://openalex.org/W2002436269","https://openalex.org/W2168743774","https://openalex.org/W4300944220"],"abstract_inverted_index":{"Abstract.":[0],"This":[1,61],"paper":[2],"develops":[3],"least-squares":[4,30,48,151],"methods":[5,81,110],"for":[6,67,126],"the":[7,27,36,39,46,55,93,102,106,140,146],"solution":[8,80],"of":[9,71,131,142],"linear":[10,157],"elastic":[11],"prob-lems":[12],"in":[13,54,136,145],"both":[14],"two":[15],"and":[16,38,52,116],"three":[17],"dimensions.":[18],"Our":[19,96],"main":[20],"approach":[21,105],"is":[22,43,50],"defined":[23],"by":[24],"simply":[25],"applying":[26],"L2":[28],"norm":[29,120],"principle":[31],"to":[32,91,138],"a":[33,127],"stress-displacement":[34],"system:":[35],"constitutive":[37],"equilibrium":[40],"equations.":[41],"It":[42,76],"shown":[44],"that":[45,111],"homogeneous":[47],"functional":[49],"elliptic":[51],"continuous":[53],"H(div;":[56,72],"\u2126)d":[57,73],"\u00d7":[58,74],"H1(\u2126)d":[59],"norm.":[60],"immediately":[62],"implies":[63],"optimal":[64,78],"error":[65],"estimates":[66],"finite":[68,86,154],"ele-ment":[69],"subspaces":[70],"H1(\u2126)d.":[75],"admits":[77],"multigrid":[79],"as":[82],"well":[83],"if":[84],"Raviart\u2013Thomas":[85],"element":[87,155],"spaces":[88],"are":[89,121,134],"used":[90],"approximate":[92],"stress":[94],"tensor.":[95],"method":[97,144],"does":[98],"not":[99],"degrade":[100],"when":[101],"material":[103],"properties":[104],"incompressible":[107,147,159],"limit.":[108,148],"Least-squares":[109],"impose":[112],"boundary":[113],"conditions":[114],"weakly":[115],"use":[117],"an":[118],"inverse":[119],"also":[122],"considered.":[123],"Numeri-cal":[124],"results":[125],"benchmark":[128],"test":[129],"problem":[130],"planar":[132],"elasticity":[133],"included":[135],"order":[137],"illustrate":[139],"robustness":[141],"our":[143],"Key":[149],"words.":[150],"method,":[152,156],"mixed":[153],"elasticity,":[158],"limit":[160]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}