{"id":"https://openalex.org/W2006617763","doi":"https://doi.org/10.1137/s003614290139696x","title":"First-Order System Least Squares for the Stress-Displacement Formulation: Linear Elasticity","display_name":"First-Order System Least Squares for the Stress-Displacement Formulation: Linear Elasticity","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2006617763","doi":"https://doi.org/10.1137/s003614290139696x","mag":"2006617763"},"language":"en","primary_location":{"id":"doi:10.1137/s003614290139696x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614290139696x","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/I4210133528","display_name":"Leibniz University of Applied Sciences","ror":"https://ror.org/03eqwj662","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210133528"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gerhard Starke","raw_affiliation_strings":["Leibniz University of Hanover"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Leibniz University of Hanover","institution_ids":["https://openalex.org/I4210133528"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.0332,"has_fulltext":false,"cited_by_count":71,"citation_normalized_percentile":{"value":0.94990395,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"41","issue":"2","first_page":"715","last_page":"730"},"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":1.0,"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":1.0,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8493189215660095},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7559391856193542},{"id":"https://openalex.org/keywords/linear-elasticity","display_name":"Linear elasticity","score":0.7078645825386047},{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.6246511340141296},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6223028898239136},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.6037111878395081},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.4918944835662842},{"id":"https://openalex.org/keywords/stress","display_name":"Stress (linguistics)","score":0.473862886428833},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.46862295269966125},{"id":"https://openalex.org/keywords/cauchy-stress-tensor","display_name":"Cauchy stress tensor","score":0.4676501452922821},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.4669797122478485},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.38055527210235596},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36993128061294556},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.0995093584060669},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.09423881769180298},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.058359891176223755},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.05381685495376587}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8493189215660095},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7559391856193542},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.7078645825386047},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.6246511340141296},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6223028898239136},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.6037111878395081},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.4918944835662842},{"id":"https://openalex.org/C21036866","wikidata":"https://www.wikidata.org/wiki/Q181767","display_name":"Stress (linguistics)","level":2,"score":0.473862886428833},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.46862295269966125},{"id":"https://openalex.org/C171338203","wikidata":"https://www.wikidata.org/wiki/Q13409892","display_name":"Cauchy stress tensor","level":2,"score":0.4676501452922821},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.4669797122478485},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.38055527210235596},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36993128061294556},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0995093584060669},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.09423881769180298},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.058359891176223755},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05381685495376587},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s003614290139696x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614290139696x","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:10.1.1.24.8982","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.8982","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/lselas.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.502.9358","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.502.9358","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/03CaiStarke.pdf","raw_type":"text"},{"id":"pmh:oai:bibcyt.ucla.edu.ve:T070300013551/16","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300013551/16&Nombrebd=Bciucla","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1492326914","https://openalex.org/W1852082788","https://openalex.org/W1965034652","https://openalex.org/W1992358193","https://openalex.org/W2014744421","https://openalex.org/W2041523977","https://openalex.org/W2042217043","https://openalex.org/W2046000001","https://openalex.org/W2051570063","https://openalex.org/W2061175874","https://openalex.org/W2062618977","https://openalex.org/W2073123170","https://openalex.org/W2073774784","https://openalex.org/W2075887353","https://openalex.org/W2079318234","https://openalex.org/W2099656682","https://openalex.org/W2105816608","https://openalex.org/W2145344822","https://openalex.org/W2489432230","https://openalex.org/W2505920944","https://openalex.org/W3149667697","https://openalex.org/W4205777361","https://openalex.org/W4241914827","https://openalex.org/W4292166829","https://openalex.org/W4297914047"],"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/W4312246552"],"abstract_inverted_index":{"Abstract.":[0],"This":[1],"paper":[2],"develops":[3],"a":[4],"least-squares":[5,19,55,78],"finite":[6,51,56,79],"element":[7,52,57,80],"method":[8,58],"for":[9],"linear":[10,82],"elasticity":[11],"in":[12,36,64,72],"both":[13],"two":[14],"and":[15,44,49,68],"three":[16],"dimensions.":[17],"The":[18],"functional":[20],"is":[21,59],"based":[22],"on":[23],"the":[24,28,32,37,41,47,65,73],"stress-displacement":[25],"formulation":[26],"with":[27],"symmetry":[29],"condition":[30],"of":[31],"stress":[33],"tensor":[34],"imposed":[35],"first-order":[38],"system.":[39],"For":[40],"respective":[42],"displacement":[43],"stress,":[45],"using":[46],"Crouzeix\u2013Raviart":[48],"Raviart\u2013Thomas":[50],"spaces,":[53],"our":[54],"shown":[60],"to":[61],"be":[62],"optimal":[63],"(broken)":[66],"H1":[67],"H(div)":[69],"norms":[70],"uniform":[71],"incompressible":[74,84],"limit.":[75],"Key":[76],"words.":[77],"method,":[81],"elasticity,":[83],"limit":[85]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":9},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
