{"id":"https://openalex.org/W2077172129","doi":"https://doi.org/10.1090/s0025-5718-07-01998-9","title":"Mixed finite element methods for linear elasticity with weakly imposed symmetry","display_name":"Mixed finite element methods for linear elasticity with weakly imposed symmetry","publication_year":2007,"publication_date":"2007-07-26","ids":{"openalex":"https://openalex.org/W2077172129","doi":"https://doi.org/10.1090/s0025-5718-07-01998-9","mag":"2077172129"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-07-01998-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01998-9","pdf_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01998-9/S0025-5718-07-01998-9.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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01998-9/S0025-5718-07-01998-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Douglas N. Arnold","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Douglas N. Arnold","raw_affiliation_strings":["Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, Minnesota 55455"],"affiliations":[{"raw_affiliation_string":"Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, Minnesota 55455","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Richard S. Falk","orcid":null},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard S. Falk","raw_affiliation_strings":["Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8019"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8019","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"last","author":{"id":null,"display_name":"Ragnar Winther","orcid":null},"institutions":[{"id":"https://openalex.org/I184942183","display_name":"University of Oslo","ror":"https://ror.org/01xtthb56","country_code":"NO","type":"education","lineage":["https://openalex.org/I184942183"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Ragnar Winther","raw_affiliation_strings":["Centre of Mathematics for Applications and Department of Informatics, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway"],"affiliations":[{"raw_affiliation_string":"Centre of Mathematics for Applications and Department of Informatics, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway","institution_ids":["https://openalex.org/I184942183"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I130238516"],"apc_list":null,"apc_paid":null,"fwci":10.2833,"has_fulltext":true,"cited_by_count":237,"citation_normalized_percentile":{"value":0.98747691,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"76","issue":"260","first_page":"1699","last_page":"1724"},"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":0.569599986076355,"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":0.569599986076355,"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":0.1347000002861023,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.04439999908208847,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/finite-element-method","display_name":"Finite element method","score":0.7156000137329102},{"id":"https://openalex.org/keywords/linear-elasticity","display_name":"Linear elasticity","score":0.65420001745224},{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.6383000016212463},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5752999782562256},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5220000147819519},{"id":"https://openalex.org/keywords/displacement-field","display_name":"Displacement field","score":0.4779999852180481},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.4505000114440918},{"id":"https://openalex.org/keywords/nonlinear-elasticity","display_name":"Nonlinear elasticity","score":0.40119999647140503}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8375999927520752},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7156000137329102},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.65420001745224},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.6383000016212463},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5752999782562256},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5454000234603882},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5220000147819519},{"id":"https://openalex.org/C29660869","wikidata":"https://www.wikidata.org/wiki/Q5282615","display_name":"Displacement field","level":3,"score":0.4779999852180481},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.4505000114440918},{"id":"https://openalex.org/C2983365874","wikidata":"https://www.wikidata.org/wiki/Q193514","display_name":"Nonlinear elasticity","level":3,"score":0.40119999647140503},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.39739999175071716},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37299999594688416},{"id":"https://openalex.org/C2778414698","wikidata":"https://www.wikidata.org/wiki/Q7623438","display_name":"Stress field","level":3,"score":0.3206000030040741},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3158999979496002},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.31369999051094055},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C153658351","wikidata":"https://www.wikidata.org/wiki/Q746264","display_name":"Constant function","level":3,"score":0.3003000020980835},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.26420000195503235}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-07-01998-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01998-9","pdf_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01998-9/S0025-5718-07-01998-9.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:arXiv.org:math/0701506","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0701506","pdf_url":"https://arxiv.org/pdf/math/0701506","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-07-01998-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01998-9","pdf_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01998-9/S0025-5718-07-01998-9.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":[],"awards":[{"id":"https://openalex.org/G5019176702","display_name":"Numerical Solution of Partial Differential Equations and Applications","funder_award_id":"0411388","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"},{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2077172129.pdf","grobid_xml":"https://content.openalex.org/works/W2077172129.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W6743369041"],"related_works":["https://openalex.org/W1998445432","https://openalex.org/W2159787769","https://openalex.org/W2153132837","https://openalex.org/W749947773","https://openalex.org/W4280600153","https://openalex.org/W2094134692","https://openalex.org/W2094939306","https://openalex.org/W2075973912","https://openalex.org/W2070979601","https://openalex.org/W2564651828"],"abstract_inverted_index":{"In":[0],"this":[1,55,87],"paper,":[2],"we":[3,93,126],"construct":[4,127],"new":[5,68,95],"finite":[6,97],"element":[7],"methods":[8,32],"for":[9,99],"the":[10,13,40,48,52,76,81,90,109,120,138,147],"approximation":[11],"of":[12,15,39,64,75,108],"equations":[14],"linear":[16,134],"elasticity":[17,77,100],"in":[18,89,101],"three":[19],"space":[20],"dimensions":[21],"that":[22,44],"produce":[23],"direct":[24],"approximations":[25],"to":[26,116,136,145],"both":[27],"stresses":[28],"and":[29,141],"displacements.":[30],"The":[31],"are":[33],"based":[34],"on":[35,51],"a":[36,62,66,72,102],"modified":[37],"form":[38],"Hellinger\u00e2\u0080\u0093Reissner":[41],"variational":[42],"principle":[43],"only":[45,132],"weakly":[46],"imposes":[47],"symmetry":[49],"condition":[50],"stresses.":[53],"Although":[54],"approach":[56],"has":[57],"been":[58],"previously":[59,122],"used":[60],"by":[61],"number":[63],"authors,":[65],"key":[67],"ingredient":[69],"here":[70],"is":[71],"constructive":[73],"derivation":[74],"complex":[78],"starting":[79],"from":[80,105],"de":[82,110],"Rham":[83,111],"complex.":[84,112],"By":[85],"mimicking":[86],"construction":[88],"discrete":[91],"case,":[92],"derive":[94],"mixed":[96],"elements":[98,114,135],"systematic":[103],"manner":[104],"known":[106],"discretizations":[107,129],"These":[113],"appear":[115],"be":[117],"simpler":[118],"than":[119],"ones":[121],"derived.":[123],"For":[124],"example,":[125],"stable":[128],"which":[130],"use":[131],"piecewise":[133,142],"approximate":[137,146],"stress":[139],"field":[140],"constant":[143],"functions":[144],"displacement":[148],"field.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":24},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":19},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":15},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2016-06-24T00:00:00"}
